if 5x = 3y = 16 and xy = 2 , find the value fot 125 x^3 + 27 y3
Answers
Given : 5x + 3y= 16 and xy= 2.
To Find : Value of 125x³ + 27y³
Solution:
(a + b)³ = a³ + b³ + 3ab(a + b)
5x + 3y= 16
Taking cube both sides
=> (5x + 3y)³ = 16³
=> 125x³ + 27y³ + 3(5x)(3y)(5x + 3y) = 16³
=> 125x³ + 27y³ + 45xy(5x + 3y) = 16³
5x + 3y= 16 and xy = 2
=> 125x³ + 27y³ + 45(2)(16) = 16³
=> 125x³ + 27y³ + 90(16) = 16³
=> 125x³ + 27y³ = 16³ - 90(16)
=> 125x³ + 27y³ = 16 ( 16² - 90)
=> 125x³ + 27y³ = 16 (256 - 90)
=> 125x³ + 27y³ = 16 (166)
=> 125x³ + 27y³ = 2656
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Answer:
sir ,but in the question it was given that 5x=3y=16.Then, how you can change it into 5x + 3y = 16....I have given the answer at first but you have deleted my answer.Was my answer wrong ? I beg clear concept on this question from you. Thank you.