5. Show that: b>0 and a <0 such that a² = b⇒a= -√b. 6. Prove that there are real numbers a and b, such that (a + b)² = a² + b²

Q: Prove: Let a &gt; 0 and b &gt; 0 then either a &gt; 0 and b &gt; 0 or a &lt; 0 and b &lt; 0. where a…

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Q: 19find all zeroS fx)=x3 +Hx*tX +H

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Q: b) Prove that + ≥ 2, for any nonzero real numbers a and b.

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Q: 2. Solve: 3 -X-2 x²- 11 1 X x=²=₂+x²= 1² and state any NPV's. X-2 X+1

A: This is question of calculus.Here one equation is given We have to solve it.And state the…

Q: Let a and b be positive integers. If ax + by = c has an integer solution (x, y), it is necessarily…

A: Consider the given equation. Find the characteristic for c if a, b are positive integers and ( x, y…

Q: 66. Let f(x) = ax? + bx + c (a + 0). By completing the square in x, show that 4aс - f(x) = a x + 2a…

A: Given,           Let fx=ax2+bx+c a≠0

Q: Prove that a b + 2c + 3d + c+ 2d + 3a Let a, b, c, d be positive real numbers. C d + 2a + 3b + d a +…

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Q: Exercise Simplify : 1) |1– v7| + (V7 – 3)2 – |-2/7| + |4² – 3 x 61. 7- 3)2 - |-2V7|+ |4? – 3 × 6|.…

A: Absolute value means distance , so if we say that |x| we mean that the distance between x and the…

Q: Let a, b, c and d be distinct real numbers. Show that the equation (x – b) (x – c)(x - d) + (x –…

A: Rolle's theorem:-

Q: Calculate Vv and V x v. a) OV-v=-2x²yz and V × v = 0 b) OV v = 2yz + 3 and V x v = -2xi+ 2xyj +…

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Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: 5. if we have two polynomials pl=3x5 + 8x* – 2x2 + 4x + 1 p2= 2x6 + 3x* – x² + 4x Find:- Your answer…

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Q: Find the difference quotient, a) 5h²+2a+h+6 h Ob) 10a + 5h + 1 O c) 10a +1 Od) 5h + 1 f(a+h)-f(a) h…

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Q: (a+b)(a+ba)(ao³ + bw) = a' +b*

A: The question is wrong. Ask your guide for correction.

Q: 1 1. -to prove that x+y|# | x|+ | y| for all real numbers d) Use x = and y = %3D x and y.

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Q: Prove there is no real number a such that 28 + x6 + 1 = 2x³

A: The given equation .The aim is to prove the equation has no real solutions.

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: 19 a) Edur 1+2r 1 b) (1 +25), | E dr

A: We will solve  the integration.

Q: 59. Let a, c +0. Show that the roots of ax? + bx +c = 0 cx? + bx + a =0 and are reciprocals of each…

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Q: Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a – b).

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Q: Determine all of the subfields of Q(√2).

A: To find all subfields of Q2

Q: Prove that if b+ 6 < 0, then x + bx + 5= 0 has at least one real solution.

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Q: 16. Find the set of real values of x for which:/3 - 2x/S/x + 4/. N.Find the set of values of x for…

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Q: Q1) Write the following in scientific notation 1.) 1.234*10 2) -8.765*10402 3.) 1015

A: Given notation can be solved by formulaes

Q: Let A be a randomly selected number from the interval (-5,4). What is the probability that the…

A: We can solve this problem by finding the values of A that will result in the quadratic equation…

Q: show that the Squa giver by IN A+ 4

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Q: ) List all the possible rational zeros of flx) = 2r - 5x + 2x + 6 A) 2, ±3, 26 * 21, 2, 23 ±1, C)…

A: Topic = Algebra

Q: answer only 9

A: Step 1: Step 2: Step 3: Step 4:

Q: Show that the statement below is true. There exist real numbers x and y such that √(x+y)=√x+√y.

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Q: 1- Prove that (a) |A× B|² = |A|2|B|? – (A · B)² (b) (Ax B)(C × D) = (A· C)(B· D) – (A · D)(B · C)…

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Q: A) |2x² + 5x + 1 = 1 B) 12/1 x-1 x+1 C) 5x + | ≥ 1

A: