Question #53d32

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Answer 1 · 2017-03-29T11:40:31

$58975/20736, or, -58975/20736.$

$x+1/x=2 1/12=25/12.$

$rArr (x^2+1)/x=25/12.$

$rArr 12x^2+12=25x.$

$rArr 12x^2-25x+12=0.$

$rArr 12x^2-16x-9x+12=0,...[16xx9=144, 16+9=25].$

$rArr 4x(3x-4)-3(3x-4)=0.$

$rArr (3x-4)(4x-3)=0.$

$rArr x=4/3, or, x=3/4.$

$x=4/3rArrx^4-1/x^4=(4/3)^4-(3/4)^4=256/81-81/256=58975/20736.$

$x=3/4rArrx^4=1/x^4=(3/4)^4-(4/3)^4=-58975/20736.$

Enjoy Maths.!