Question

Q.19 If x +y =12 and xy =14, find the value of (x²+y?)​

Answer 1

Question :

$\large{⟼}$ If ${x\:+\:y\:=\:12}$ and ${xy\:=\:14}$ , then find the value of ${x²\:+\:y²}$ .

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Given :

$\large{⟼}$ Value of the sum of x and y is 12 and the product of the terms x and y is 14 .

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⟶$\large\bf{\mathtt{\underline{x+y=12}}}$

⟶$\large\bf{\mathtt{\underline{xy=14}}}$

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To Find :

⟶$\large\bf{\mathtt{\underline{x²+y²=¿}}}$

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We know :

$\large\bf{\mathtt{\underline{\red{(ab)²=a²+b²+2ab}}}}$

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Solution :

Using above identity ( x + y )² becomes ,

⟶ $\large\bf{\mathtt{\boxed{\boxed{\green{(x+y)²=x²+y²+2xy}}}}}$

⊙ || according to substitution :

we get ,

⟹ $\large\bf{\mathtt{\red{(12)²=x²+y²+2×14}}}$

⟹ $\large\bf{\mathtt{144=x²+y²+28}}$

⟹ $\large\bf{\mathtt{x²+y²=144-28}}$

⟹ $\large\bf{\mathtt{\green{x²+y²=116}}}$

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Required Answer :

$\large\bf{\mathbb{\boxed{\underline{\underbrace{<strong>x²</strong><strong>+</strong><strong>y²</strong><strong>=</strong><strong>1</strong><strong>1</strong><strong>6</strong>}}}}}$

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