Question

x+1/x=7 then find x-1/x​

Answer 1

Answer:

-5

Step-by-step explanation:

• find the value of x so the value find out by solving

x+1/x = 7

x =1/6

• put the value of x in

x-1/x

so we get -5 (ans.)

Answer 2

Given,

$\sf{x + \frac{1}{x} = 7 }$

To find:

$\sf{x - \frac{1}{x} }$

The following formulas are used:

•(a+b)²=a²+2ab+b²

•(a-b)²=a²-2ab+b²

Now,

$\sf{x + \frac{1}{x} = 7 } \\ \\ \sf{squaring \: on \: both \: sides} \\ \\ \implies \: \sf{(x + \frac{1}{x}) {}^{2} = 49 } \\ \\ \implies \: \sf{x {}^{2} + \frac{1}{x {}^{2} } + 2 = 49 } \\ \\ \implies \: \sf{x {}^{2} + \frac{1}{x {}^{2} } = 47 }$

$\sf{let \: us \: assume \: x - \frac{1}{x} = y } \\ \\ \sf{squaring \: on \: both \: sides} \\ \\ \implies \: \sf{y {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } - 2 } \\ \\ \implies \: \sf{y {}^{2} = 45 } \\ \\ \implies \: \: \underline{\boxed{\sf{y = 3 \sqrt{5} }}}$