(a) Prove that any odd number greater than one can be expressed as the difference of the squares of two consecutive positive integers.

Q: Show that the square of any integer is of the form 3m or 3m+1 but not of form 3m+2.

A: Proof :-

Q: The Product of two positive decimals each less than 1 is never less than any of the factors. True or…

A: To check for The Product of two positive decimals each less than 1 is never less than any of the…

Q: Evaluate. (2x+1)/x2+x-1  with endpoints 3 and 1.

A: Consider the given function: fx=2x+1x2+x-1 Now plug-in the value x=3 in the function. This gives,…

Q: The number of zeros of the polynomial x? + 2x +3 in Z, is: 1 None 4.

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Q: Two negative integers are 8 units apart on the number line and have a product of 308. Which…

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Q: Three consecutive even integers are such that the square of the third is 76 more than the square of…

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Q: According to Descartes' Rule of Signs, how many negative zeroS could the polynomial æ4 – 3x³ – 2x² +…

A: According to Descartes's rule of signs, maximum number of positive real root of a polynomial…

Q: Express as a polynomial. (r 2 + 8r - 2-)(r 2 + 3r - 1)

A: Given expression:                         (r2+8r-2)(r2+3r-1)

Q: Write out a careful proof of the fact that the square of an odd number is odd.

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Q: Find two positive numbers a and b such that 2a + 3b = 1 and so that a3 + b2 is as small as possible.

A: Find  two positive numbers a and b such that 2a + 3b =1 and so that a3  + b2  is a small as…

Q: Determine the Fourier Series of the function f(x)= |x|, -3 ≤ x ≤ 3, f(x) = f(x+6).

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Q: If two is subtracted from the square of a number, the result is two. Hind all such numbers. If there…

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Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: 9. Find values of the 800k of polynomial 1- 42+9x +b b. -9 and if 3-42²+9x +6. a and ane

A: Given the polynomial  x3−4x2+ax+b

Q: For the following polynomial, one zero is given. Find the remaining zeros. P(x)=x +7x - 144, 4i is a…

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Q: -21a b6 – 42a®b5 + 7a>b4 -7a+b5 2x3+ 7x2 + 10х + 8 х+2

A: The solution for the above question is as shown below.

Q: If the conjugate of a zero (which is 2+3i), would it still be 2-3i and would 2-3i count as one of…

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Q: represent, 5 x 17=85, 5 x 29=145, 13 x 17=221 as a sum of two squares according to the formula n1 x…

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Q: Find the square root of the product of (3+ j4) and (2+ j8)

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Q: Find all positive integers of x in the equation x⁵+2x-5 > 19.

A: The solution for the given inequality is determined as shown below.