Question

if x+y=5 and xy=10 then find the value of x²+y²
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Answer 1

Step-by-step explanation:

refer to attachment for answer

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Answer 2

$\bf \: {x}^{2} + {y}^{2} = 5$

Given:

• If $x + y = 5$ and
• $xy = 10$

To find:

• Find the value of ${x}^{2} + {y}^{2}$.

Solution:

Concept/Formula to be used:

$\bf ( {x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

Step 1:

Squaring both sides.

As, it is given ,$x + y = 5$

Square both sides;

$( {x + y)}^{2} = ( {5)}^{2}$

Open identity in the left hand side.

${x}^{2} + {y}^{2} + 2xy = 25$

$\bf {x}^{2} + {y}^{2} = 25 - 2xy ...eq1$

Step 2:

Find the value of x²+y².

Put the value of xy in eq1.

${x}^{2} + {y}^{2} = 25 - 2(10)$

${x}^{2} + {y}^{2} = 25 - 20$

$\bf \: {x}^{2} + {y}^{2} = 5$

Thus,

The value of x²+y² is 5.

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(1) 1 (2) 0

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