Question

prove that 9*x square + 1/x square - 9*x+1/x - 52 = 0​

Answer 1

Answer:

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Step-by-step explanation:

9(x^2=1/x^2) -9(x+1/x) -52=0

Let x+1/x=y

squaring on both sides

x^2+1/x^2+2=y^2

==> x^2+1/x^2=y^2-2

putting these values in the given equation

9(y^2-2)-9y-52=0

==>9y^2-18-9y-52=0

==>9y^2-9y-70=0

==>9y^2 -30y+21y-70=0

==>3y(3y-10)+7(3y-10)=0

==>(3y-10)(3y+7)=0

==>3y-10=0 or 3y+7=0

==>y=10/3 or y=-7/3

==>x+1/x= 10/3 or -7/3

==>x^2+1/x=10/3 or -7/3

==>3x^2-10x+3=0 or 3x^2+7x+10=0

==>3x^2-9x-x+3=0 or x= -7+√(-7)^2-4(3)(3)/2(3)

==>3x(x-3)-1(x-3)=0 or x=-7+√3/6

==> (x-3)(3x-1)=0

==>x=3 and x=1/3