If x>0 and x²+1/9x²=25/36, find x³+1/27x³
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Given that :
x² + 1/9x² = 25/36
Adding and subtracting 2/3
( x )² + ( 1/3x )² + 2( x )( 1/3x ) - 2/3 = 25/36
( x + 1/3x )² = 49/36
( x + 1/3x ) = 7/6
Cubing both sides ,
x³ + 1/27x³ + 3( x )( 1/3x )( x + 1/3x ) = 343/216
Final answer : x³ + 1/27x³ = 91/216
AsutoshDikhit:
Okay, thanks.
While taking the square root , I've taken only the +ve one i.e. +7/6 hence getting 91/216 as the answer
Though if you take -7/6 you'll get -91/216
Hope you got it
Yeah, thanks again for helping me out.
You're most welcome
Ask me if any doubts in MATHEMATICS ^_^
I don't usually have any doubts in maths. But yes I'll ask if i have one.
Surely
I'd be glad to help
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