Question

. If x - y = 6 and xy = 10 find the value of x^2+ y^2​

Answer 1

Solution

Given :-

• x - y = 6 ________(1)
• xy = 10__________(2)

Find :-

• Value of x² + y²

Explanation

Using Formula.

★(x - y)² = x² + y² - 2xy

Keep all above by equ(1) & equ(2) values

==> (6)² = x² + y² - 2 × 10

==> 6 × 6 = x² + y² - 20

==> 36 = x² + y² - 20

==> x² + y² = 30 + 20

==> x² + y² = 50

Hence

• Value of x² + y² be 50.

___________________

Answer 2

x - y = 6

=> x = 6 + y. ••••••••• equation 1.

xy = 10

=> y = 10/x. ••••••••• equation 2.

substituting the value of y in equation 1

x = 6 + 10/x

x² = 6x + 10. •••••••••• equation 3

substituting the value of x in equation 2

y = 10/6+y

=> y(6+y) = 10

=> 6y + y² = 10

=> y² = 10 - 6y. •••••••••• equation 4

from equation 3 and 4

x² + y² = 6x + 10 + 10 - 6y

= 20 + 6x - 6y

= 20 +6 ( x - y )

= 20 + 6 × 6 (according to the question)

= 20 + 36

= 56