Question

If x - y = 10 and x² + y² = 148 then find x² - y²...
please explain step by step​

Answer 1

Step-by-step explanation:

x - y = 10

x = 10 + y

now,

x² + y² = (10 + y ) ² + y² = 148

= 100 + y² + 20y + y² = 148

= 20y + 2y² = 148 - 100

= 20y + 2y² = 48

= y² + 10y - 24 = 0

= y² + 12y - 2y - 24 = 0

= y ( y + 12) - 2 ( y + 12) = 0

= (y-2)(y+12) = 0

:. y = 2 or y = -12

thus, taking the positive value of y

x = 10 + 2 = 12

now ,

x² - y² = (12)² - (2)²

= 144 - 4

= 140