Question

If x/8+1/x=9/8 then find the value of x^2+64/x^2



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Answer 1

Answer:

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Step-by-step explanation:

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x9+98x6+2764x3−x+219512=0⇒512x9+(9⋅64)x6+(27⋅8)x3−512x+219=0

x9+98x6+2764x3−x+219512=0⇒512x9+(9⋅64)x6+(27⋅8)x3−512x+219=0

So

(8x3)3+3(8x3)2⋅3+3(32)⋅8x3+33−512x+219−33=0

(8x3)3+3(8x3)2⋅3+3(32)⋅8x3+33⏟−512x+219−33=0

So

(8x3+3)3=512x−219⇒(8x3+3)3=512(x−192512)=83(x−38)13.

(8x3+3)3=512x−219⇒(8x3+3)3=512(x−192512)=83(x−38)13.

So

83(x3+38)=8(x−38)13⇒x3+38=(x−38)13

83(x3+38)=8(x−38)13⇒x3+38=(x−38)13

Now Let f(x)=x3+38,f(x)=x3+38, Where f:R→R,f:R→R, Then f−1(x)=(x−38)13,f−1(x)=(x−38)13, Where f:R→Rf:R→R

So We have To solve

f(x)=f−1(x)

f(x)=f−1(x)

Now We now that f(x)f(x) and f−1(x)f−1(x) is Symmetrical about y=xy=x line.

So

f(x)=f−1(x)=x

f(x)=f−1(x)=x

So

x3+38=x⇒8x3−8x+3=0

x3+38=x⇒8x3−8x+3=0

Answer 2

Step-by-step explanation:

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