Question

If x2 + y2 = 14 and xy=5 find the value of (x+y)2.

Answer 1

given, x^2+y^2=14 ; x*y=5
so, (x+y)^2=x^2+y^2+2*x*y
=14+2*5 = 24
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Answer 2

Answer:

$(x+y)^{2}$ = 24

Step-by-step explanation:

Given:

$x^{2} +y^{2} =14$

$xy=5$

Find:

$(x+y)^{2}$

Solution:

We know that, $(x+y)^{2} = x^{2} +2xy + y^{2}$

Given that:

$x^{2} +y^{2} =14$

⇒ $x^{2} +y^{2} +2xy = 14+2xy$        (Adding $2xy$ on both sides)

⇒ $(x+y)^{2} = 14+2xy$    

⇒ $(x+y)^{2} = 14+(2\times 5)$             ( ∵ $xy=5$ )

⇒ $(x+y)^{2} = 14+10$

⇒ $(x+y)^{2} = 24$

This problem deals with the basic algebraic identities. Some other algebraic identities are:

• $(x-y)^{2} = x^{2} -2xy+y^{2}$
• $(x+y)(x-y)=x^{2} -y^{2}$

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