Question

A2 + 1/a2 = 14 find value of a - 1/a

Answer 1

Answer:

given,a^2+1/a^2=14;

a^2+1/a^2-2*a*1/a=14-2;

(a-1/a)^2=12;

a-1/a=√12;

a-1/a=2√3

Answer 2

The value of a-1/a is 2√3.

Given,

The value of a²+1/a² = 14.

To Find,

The value of a-1/a.

Solution,

The given expression is

a²+1/a² = 14

Now, we will subtract 2 from both sides of the equation

a²+1/a²-2 = 14-2

a²+1/a²-2(a*1/a) = 12 {The va;ue of a*1/a is 1, so it won't affect the equation}

Using the formula

a²+b²-2ab = (a-b)²

So, the equation becomes

(a-1/a)² = 12

a-1/a = √12

a-1/a = 2√3

Hence, the value of a-1/a is 2√3.

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