Question

If x + y = 7 and xy = 12, find x² + y².

Answer 1

Answer:25

Step-by-step explanation:(x+y)^2=x^2+y^2+2xy.

(7)^2=x^2+y^2+2×12

49=x^2+y^2+24

49-24=x^2+y^2

25=x^2+y^2

Answer 2

If x + y = 7 and xy = 12 then $x^2 + y^2 = 25$

Solution:

Given that,

x + y = 7

xy = 12

To find: $x^2 + y^2$

From given,

$x + y = 7\\\\\text{Take square on both sides }\\\\(x+y)^2 = 7 ^2\\\\Expand\\\\x^2 + y^2 + 2xy = 49\\\\Substitute\ xy = 12\\\\x^2 + y^2 + 2(12) = 49\\\\x^2 + y^2 + 24 = 49\\\\x^2 + y^2 = 49 - 24\\\\x^2 + y^2 = 25$

Thus, $x^2 + y^2 = 25$

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