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What will be the value of xy, if x2 + y2 = 45 and x - y = 5?
- A10
- B15
- C20
- D25
Answer not set
Discussion 1
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CCommunity
Given x - y = 5 and x2 + y2 = 45
From the Algebraic Identity, we know that (x - y)2 = x2 + y2 - 2xy
xy = [(x2 + y2) - (x - y)2]/2 ----(1)
Substituting the values of (x - y) and (x2 + y2) in Equation 1, we get
xy = [45 - (5)2]/2
⇒ xy = (45 - 25)/2 = 20/2 = 10
∴ Value of xy = 10
From the Algebraic Identity, we know that (x - y)2 = x2 + y2 - 2xy
xy = [(x2 + y2) - (x - y)2]/2 ----(1)
Substituting the values of (x - y) and (x2 + y2) in Equation 1, we get
xy = [45 - (5)2]/2
⇒ xy = (45 - 25)/2 = 20/2 = 10
∴ Value of xy = 10