Complete-the-square-in-y-2-8y-9k-and-hence-find-the-value-of-k-that-makes-it-a-perfect-square-

Question Number 31306 by pieroo last updated on 05/Mar/18

Complete the square in y^{2} + 8 y + 9 k and hence find the

value of k that makes it a perfect square .

Answered by MJS last updated on 05/Mar/18

{(a + b)}^{2} = a^{2} + 2 a b + b^{2}

a^{2} = y^{2} \Rightarrow a = y

2 a b = 8 y

2 b y = 8 y

b = 4

{(y + 4)}^{2} = y^{2} + 8 y + 16

16 = 9 k

k = \frac{16}{9}

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