Question

If x+y=10 and x-y=4, find the value of x2+y2

Answer 1

Answer:

x+y=10

x-y=4

by elimination method

2x=14

x=7

now fill value of x in equation 1

7+y=10

y=3

7×2+(3)×2

14-6 =8

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Answer 2

The value of x² + y² is 58.

Step-by-step explanation:

Given: $x+y=10 \ \text{and} \ x-y=4$

To Find: $x^{2} + y^{2}$

Solution:

• Finding the value of x² + y²

By using the elimination method, we get,

$\ \ x + y = \ 10\\{} \ \ x - y = \ \ 4\\- {} \ + \ \ \ \ -\\\overline{\ 0 \ + \ 2y = \ 6 \ \ }$

$\Rightarrow 2y = 6\\\Rightarrow y = 3$

Now, substituting y = 3 in either of the given equations, we get

$\Rightarrow x - y = 4$ $\Rightarrow x = 4 + y$ $\Rightarrow x = 4 + 3 = 7$

$\Rightarrow x = 7$

Now, substituting x = 7 & y = 3 to find the value of x² + y²

Therefore, $x^{2} + y^{2} = (7)^{2} + (3)^{2} = 49+ 9 = 58$

$\Rightarrow x^{2} + y^{2} = 58$

Hence, the value of x² + y² is 58.