Question

if( x^2+y^2)=25 and xy=8, then fund the value of x+y and x-y.​

Answer 1

Answer:

${x}^{2} + {y}^{2} = 25 \\ xy = 8 \\ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ {( x + y)}^{2} = 25 + 2 \times 8 \\ {(x + y)}^{2} = 25 + 16 \\ x + y = \sqrt{25 + 16} = \sqrt{41} \\ {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ {(x - y)}^{2} = 25 - 2 \times 8 \\ {(x - y)}^{2} = 9 \\ x - y = \sqrt{9} = 3 \: or \: - 3$