perplexus.info :: Just Math : Find the value of a

Find the value of a (Posted on 2024-09-18)

Given that:
F(x) = x²+10x, and:
F(F(a)) = 11

Find the value of a.

No Solution Yet Submitted by K Sengupta

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solution

| Comment 1 of 2

F(x) = x^2+10x

F(F(x)) = (x^2+10x)^2 + 10(x^2+10x)

= x^4 + 20x^3 + 100x^2 + 10x^2 + 100x

= x^4 + 20x^3 + 110x^2 + 100x

If F(F(a)) = 11, then a^4 + 20a^3 + 110a^2 + 100a - 11 = 0

(a^2 + 10a - 1)*(a^2 + 10a + 11) = 0

a = -5 ± √(26)

a = -5 ± √(14)

Posted by Larry on 2024-09-18 12:21:58

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