Question

if x=8+3√7. find x-1/x

Answer 1

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Answer 2

Answer:

Given: x=8+3√7

To find: x-1/x

Step-by-step explanation:

Let z = √x - 1/√x

So squaring both the sides,

x = 8 + 3√7

∴ 1/x = 1/(8 + 3√7)

∴ 1/x = 8 - 3√7 {By rationalization}

• A radical or imaginary number can be removed from the denominator of an algebraic fraction by a procedure known as rationalisation.
• That is, eliminate the radicals from a fraction to leave only a rational integer in the denominator.

z2 = x + 1/x - 2

therefore, z2 = (8 + 3√7) + (8 - 3√7) - 2 = 14

∴ z = √14

Hence, the answer is 14.

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