In class, we proved that 2 is irrational. Now, verify that (i) /3, (ii) /6, and (iii) 2+ v3 are all irrational too.

Q: 2 and B= 1 0. then Show that if A = 6. -1 2 (A + B)(A + B) # A² + 2AB + B?

A: Given that A=-1201 and B=10-12 We have to show that A+BA+B≠A2+2AB+B2

Q: Consider nonnegative integer solutions of the equation xi + x2 + x3 + x4 + x5 + æ6 = 30.

A: The non-negative integer equation is x1+x2+x3+x4+x5+x6=30Since ,xi-number varying from 0 to…

Q: Solve for u. 7 9- u+6

A: According to the question, we have to solve the expression 7u+6=-6 and find the value of u. An…

Q: If m<1 = 6(3x+1)-2, m<2= 3(x+2)+9, and m<ABC= 5(3x+5)+6, find x and m<ABC.

A: Given,           ∠1=63x+1-2           ∠2=3x+2+9            ∠ABC=53x+5+6

Q: rỉ + 10x1x2 + x = as² + ßt²

A:

Q: 13 - What is the Lagrange interpolation polynomial which passes through (2,2) and (4,6)

A: We use the Lagrange interpolation formula

Q: Prove that: n² + 3n 1 →> 2n² + 1 2 You may use any results from lectures, but you must state them…

A: (.) Given,                We find the limit.

Q: Find the exact value of (√ 13 + √2 + 7 / (3 + √2)) without the use of a calculator.

A:

Q: ;) 2r-11x-21 0 ii) x + x 22

A: 1)                                          2X2-11X-21 =0                         To solve this…

Q: 7- Find fx³√3 - 2x² dx

A:

Q: (2-V360°=-V2-3/6s

A: Given equation is: (2-√3i)z3=-√2-3√6i We have to find value of z

Q: verify that 6A = 3(2A)

A: Here given  Thus

Q: √2-1/2 is irrational

A: We need to find whether irrational or not.

Q: S(10) for √3 - 3 + 3√3+...

A:

Q: 2. Factor each trinomial by grouping. a) 2y²-y-10

A: To factor the following trinomial.

Q: Consider the function f (same as in the previous problem) defined on the interval [0, 10] as…

A: Given Data: fx=35xx∈0,53x∈5, 10-y''=λy, y0=0, y'10=0To find: cn

Q: Find the value of each of a,b,c so that 6x3 − 7x2 − x + 2 = (x − 1)(ax2 + bx + c)

A: Given equation is : 6x3-7x2-x+2=x-1ax2+bx+c To find the value a, b, and c

Q: Determine the values of (√3+ i)6 and (1 - i)8, writing your answers in a + iy form.

A: In this problem we have to determine the values of  and .

Q: Prove that the expression 2y2 - 128 is equal to 2(x2+2) (x² – 2) (x³ + 4x* + 16).

A:

Q: If a = √9+√3+1, find the value of - 100 3 3 1 a a² + +

A: Given that a=93+33+1 To find the value of 3a+3a2+1a3 .

Q: Solve for x: 3* - 6(√3)* 27 = 0

A: We see     3x - 6(√3)x - 27          = (√3)2x - 6(√3)x - 27          = (√3)2x - 9(√3)x + 3(√3)x - 27…

Q: 2. Find the difference quotient of f(x) = 4x² – 7x + 5

A:

Q: rel= = 0A 15, x² = 4(4x² - 1) If, 2 Prove that, x = √√5 +√√3

A:

Q: Show that (x? + y²)² = (x² – y²)² + (2xy)? for all real numbers x and y.

A: We have to prove algebraically that x2+y22=x2-y22+2xy2 Simplifying both the sides , we get Here ,…

Q: (x+6)-(5-2x)+2=0

A: Given equation: (x+6)-(5-2x)+2=0

Q: Prove they are equal 4 = 7(2x+ 1) - 5x -3(3x + 1)

A:

Q: Given that the equation z2 + (p + iq)z + r + is = 0, where p, q, r, s are real and non-zero has a…

A: Introduction :--

Q: if a and b are positive real number, then 0<(ab)1/2<=(a+b)/2.

A: If a and b are the positive real number Then we have to prove that  0&lt;ab≤a+b2 Since, a and b be a…