If $x - y = 7$ and $x y = 9$ , find the value of $(x^{2} + y^{2})$

Open in App

Solution

$x - y = 7$
Squaring both sides,
$(x - y)^{2} = (7)^{2} \Rightarrow x^{2} + y^{2} - 2 x y = 49 \Rightarrow x^{2} + y^{2} - 2 \times 9 = 49 \Rightarrow x^{2} + y^{2} - 2 \times 9 = 49 \Rightarrow x^{2} + y^{2} - 18 = 49 \Rightarrow x^{2} + y^{2} = 49 + 18 = 67 ∴ x^{2} + y^{2} = 67$

Suggest Corrections

125

Similar questions

If x2+xy+x=12 and y2+xy+y=18 then find the value of x-y is

x = \sqrt{7} - \sqrt{6}

y = \sqrt{7} + \sqrt{6}

x^{2} + y^{2} - x y

x + y = 9, x y = 6

x^{2} + y^{2}

(x + y + z) = 9

(x y + y z + z x) = 9

(x^{2} + y^{2} + z^{2})

If x+y=9 and xy = 20 . Find the value of x²+ y²?

Join BYJU'S Learning Program