Question

if x+1/x=4 then find x²+1/x²​

Answer 1

Answer:

x+1/x=4

x+1=4x

4x-x=1

3x=1

x=1/3

x2+1/x2

(1/3) ^2+1/(1/3) ^2

(1/9)+1/(1/9)

((1+9) /9)/(1/9)

(10) /9*9/1

10

Answer 2

To find : value of $\frac{x^{2} + 1}{x^{2} }$

Given : $\frac{x+ 1}{x} = 4$

Solution :

• As per given data we know that $\frac{x+ 1}{x} = 4$  , we have to find value of $\frac{x^{2} + 1}{x^{2} }$  

• Using transposition method we find value of $x$ from $\frac{x+ 1}{x} = 4$  .
• Therefore , solving for $x$ .

• $\frac{x+ 1}{x} = 4$  

      $x + 1 = 4x \\4x - x = 1 \\3x = 1 \\x = \frac{1}{3}$

• Now , substituting the value of $x$ in the equation $\frac{x^{2} + 1}{x^{2} }$   .

• $\frac{x^{2} + 1}{x^{2} }$  

       $= \frac{(\frac{1}{3} )^{2} +1}{(\frac{1}{3} )^{2} } \\\\= \frac{\frac{1}{9}+ 1 }{\frac{1}{9} } \\\\= \frac{\frac{1 + 9}{9} }{\frac{1}{9} } \\\\= \frac{\frac{10}{9} }{\frac{1}{9} } \\\\= \frac{10}{9} \times\frac{9}{1} \\\\ =10$

Hence , value of $\frac{x^{2} + 1}{x^{2} }$   is $10$ .