Question

If (a + b)² = 37 and ab = 5, what is

a² + b²?
A) 37
B) 32
C) 27
D) 5
cond

Answer 1

Explanation:

(a + b)² = 37

a^2 + 2ab + b^2 = 37

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ab = 5

a = (5/b)

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a^2 + 2ab + b^2 = 37

(5/b)^2 + 2(5/b)b + b^2 = 37

(25/b^2) + 10 + b^2 = 37

(25/b^2) + b^2 = 27

25 + b^4 = 27b^2

b^4 - 27b^2 + 25 = 0

I don't know how to factor this expression. The roots seem complex.