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

Question Number 130334 by pete last updated on 24/Jan/21

Complete the square in the expression

y^{2} + 8 y + 9 k and hence find the value of

k that makes it a perfect square .

Answered by TheSupreme last updated on 24/Jan/21

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

2 a = - 8 \to a = - 4

a^{2} = 16 = 9 k

k = \frac{16}{9}

Commented by pete last updated on 24/Jan/21

thanks sir

Answered by john_santu last updated on 24/Jan/21

y^{2} + 8 y + 9 k = {(y + 4)}^{2} + 9 k - 16

\Leftrightarrow 9 k - 16 = 0; k = \frac{16}{9}

Commented by pete last updated on 24/Jan/21

merci

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