If x2 + 4y2 = 53 and x - 2y = 5, then what is the value of x3 - 8y3 ?
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 335
Given :
x2 + 4y2 = 53
x - 2y = 5
Formula used :
(a - b)2 = a2 + b2 - 2ab ----- (1)
(a - b)3 = a3 - b3 - 3ab(a - b) ----- (2)
Calculations :
Using equation (1)
⇒ (x - 2y)2 = x2 + 4y2 - 2(x)(2y)
⇒ 25 = 53 - 4xy
⇒ 4xy = 28
⇒ xy = 7
Using equation (2)
⇒ (x - 2y)3 = x3 - 8y3 - 3(x)(2y)(x - 2y)
⇒ 125 = x3 - 8y3 - 6xy(5)
⇒ 125 = x3 - 8y3 -30(7)
⇒ x3 - 8y3 = 210 + 125
⇒ 335