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

$$\mathrm{Complete}\mathrm{the}\mathrm{square}\mathrm{in}{\mathrm{y}}^2+8\mathrm{y}+9\mathrm{k}\mathrm{and}\mathrm{hence}\mathrm{find}\mathrm{the}$$$$\mathrm{value}\mathrm{of}\mathrm{k}\mathrm{that}\mathrm{makes}\mathrm{it}\mathrm{a}\mathrm{perfect}\mathrm{square}.$$

Answered by MJS last updated on 05/Mar/18

$${(a+b)}^2=a^2+2ab+b^2$$$$a^2=y^2\Rightarrow a=y$$$$2ab=8y$$$$2by=8y$$$$b=4$$$${(y+4)}^2=y^2+8y+16$$$$16=9k$$$$k=\frac{16}{9}$$

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