Question

if x is equal to 1 minus root 2 find the value of x minus one by X whole to the power 4​

Answer 1

Answer:

The value of given expression is $(\frac{x-1}{x} )^{4}=4(17+12\sqrt{2} )$

Step-by-step explanation:

Given that,

The value of x is $x=1-\sqrt{2}$ and we are required to find the value of the algebraic expression given as

$(\frac{x-1}{x} )^{4}$

The above expression can be expanded into two terms as shown below

$(\frac{x-1}{x} )^{4}=(x-1)^{4}\times\frac{1}{x^{4}}$

Now before solving the problem we shall find the reciprocal of x by rationalization which is done as shown below-

$\frac{1}{x} =\frac{1}{1-\sqrt{2} } \times\frac{1+\sqrt{2} }{1+\sqrt{2} } \\=\frac{1+\sqrt{2} }{1-2} =-(1+\sqrt{2} )$

Now our given expression is calculated as shown below

$(\frac{x-1}{x} )^{4}=(x-1)^{4}\times\frac{1}{x^{4}}=(-\sqrt{2} )^{4}\times {[-(1+\sqrt{2})]^{4}} \\=4\times(3+2\sqrt{2} )^{2}=4(17+12\sqrt{2} )$

Therefore,the value of the given expression is $(\frac{x-1}{x} )^{4}=4(17+12\sqrt{2} )$

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