Question

If 81x4 + 1/x^4 = 3007 then what (6x-7)^2 =?

Answer 1

Answer: 36x² -84x +49

Step-by-step explanation: Use smilling method like this (6x-7)•(6x-7) after this.

Next is multiply and you get 36x² -84x +49.

Answer 2

The value is $(6x-7)^2=37$.

Step-by-step explanation:

Given : Equation $81x^4+ \frac{1}{x^4} =3007$

To find : What $(6x-7)^2$ ?

Solution :

We can re-write the given equation as to make it a square,

$81x^4+ \frac{1}{x^4} =3007$

$(9x^2)^2 +(\frac{1}{x^2})^2 +2\cdot 9x^2\cdot \frac{1}{x^2}=3007 +18$

Applying, $(a+b)^2=a^2+b^2+2ab$

$(9x^2+\frac{1}{x^2} )^2= 3025$

Taking square root both side,

$(9x^2+\frac{1}{x^2} )=55$

Again re-write as,

$(9x^2+\frac{1}{x^2} ) - 2\cdot 3x\cdot \frac{1}{x} =55 -6$

$(3x-\frac{1}{x} ) ^2=49$

Taking square root both side,

$3x- \frac{1}{x}=7$

$3x^2 -7x +1=0$

$3x^2 -7x =-1$

Then we open the value we have to find,

$(6x-7)^2=36 x^2 - 84 x +49$

$(6x-7)^2=12(3x^2- 7x) +49$

Substitute the value,

$(6x-7)^2=12(-1) +49$

$(6x-7)^2=37$

Therefore, the value is $(6x-7)^2=37$.

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