Question

if x+y=7/2 & xy=5/2 find x-y & x^2-y^2​

Answer 1

Answer:We know that,(x + y)² = x² + 2xy + y²and(x + y)² = x² - 2xy + y²Rewrite the above equation, we have (x - y)² = x² + y² + 2xy - 4xy = (x + y)² - 4xy.....(1)Given that,x + y = 7/2 and xy = 5/2Substitute the values of (x+ y) and (xy)(x - y)² = (7/2)² - 4(5/2)= 49/4 - 10 = 9/4→ x - y = ‡ √9/4→ a - b = ‡ (3/2)(2)We know that,x² - y² = (x + y ) (x - y)(3)From equation (2) we have,x - y = ‡ 3/2Thus equation (3) becomes,x² - y² = ( 7/2) ( ‡ 3/2 )[given x + y 7/2 ]→ x² - y² = ‡ 21/4

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Answer 2

Answer:

(x-y)^2= (x+y)^2 -4xy

=49/4. -10

9/4

so x-y= 3/2

x^2+y^2= (x+y)(x-y)

7/2×3/2

21/4