If x 1 x 7 then find the value
Asked by admin @ in Math viewed by 378 People
If x+1/x=7,then find the value of x3+1/x3
Answered by admin @
Hi ,
It is given that ,
x + 1/x = 7 -----( 1 )
*******************************************
We know the algebraic identity,
a³ + b³ + 3ab ( a + b ) = ( a + b )³
Or
a³ + b³ = ( a + b )³ - 3ab( a + b )
************************************
x³ + 1/x³ = (x + 1/x )³- 3 × x ×1/x(x + 1/x )
= ( x + 1/x )³ - 3( x + 1/x )
= 7³ - 3 × 7
= 7( 7² - 3 )
= 7 ( 49 - 3 )
= 7 × 46
= 322
I hope this helps you.
: )
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