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mars1129 [50]
3 years ago
6

Determine the value of a and b so that x^4 6x^3 +7x^2+ax+b is a perfect square

Mathematics
1 answer:
posledela3 years ago
3 0

Step-by-step explanation:

(Ax² + Bx + C)²

= (Ax² + Bx + C)(Ax² + Bx + C)

= Ax⁴ + 2ABx³ + 2ACx² + 2BCx + C².

By Comparing Coefficients, we have:

A = 1

2AB = 6

2AC = 7

2BC = a

C² = b

Solving them we get A = 1, B = 3 and C = 3.5.

Therefore a = 2BC = 2(3)(3.5) = 21,

b = C² = (3.5)² = 12.25.

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Step-by-step explanation:

<u>Out of 12 consecutive integers:</u>

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<u>Sum of 3 integers will be divisible by 4 if the remainders are:</u>

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