Question

If t+1/t=2 then t-1/t =? Please give explanation also

Answer 1

Answer:

Solve the attachment

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Answer 2

The correct answer is 0.

Given: The equation = $t+\frac{1}{t}=2$.

To Find: The value of $t-\frac{1}{t}$.

Solution:

$t+\frac{1}{t}=2$

Squaring both the sides.

$(t+\frac{1}{t})^{2} =2^{2}$

$t^{2} +\frac{1}{t^{2} }+2*t*\frac{1}{t}=4$

$t^{2} +\frac{1}{t^{2} }+2=4$

$t^{2} +\frac{1}{t^{2} }=2$

As we know the identity = $(a-b)^{2} =a^{2} +b^{2} -2ab$.

Here a = t and b =  $\frac{1}{t}$.

Add and subtract $2*t*\frac{1}{t}$ to make the identity.

$t^{2} +\frac{1}{t^{2} }-2*t*\frac{1}{t}+2*t*\frac{1}{t}=2$

$(t-\frac{1}{t} )^{2} +2*t*\frac{1}{t}=2$

$(t-\frac{1}{t} )^{2} +2=2$

$(t-\frac{1}{t} )^{2} =0$

$t-\frac{1}{t}=0$

Hence, the value of $t-\frac{1}{t}$ is 0.

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