Question

if x + 1/x = 4, let's show that x×4 + 1/x×4 = 194 .​

Answer 1

Answer:

square on both sides , do it twice it will be proved

Answer 2

Proving the value:

Step-by-step explanation:

$\ Given \ value:\\\ x+\frac{1}{x}\ = \ 4 \\\\\ Find: \\\\x^4\ + \frac{1}{x^4}\ = \ 194.\\\\\ Solution:\\\\\rightarrow \ x+\frac{1}{x}\ = \ 4 \\\\\ Square \ on \ both \ side \ of \ the \ above \ given \ value : \\\\\rightarrow (\ x+\frac{1}{x})^2\ = \ (4)^2 \\\\\therefore (a+b)^2= a^2+b^2+2.a.b$

$\rightarrow (x)^2+(\frac{1}{x})^2+ 2. x.\frac{1}{x} \ = \ 16\\\\\rightarrow (x)^2+(\frac{1}{x})^2+ 2 \ = \ 16\\\\\rightarrow (x)^2+(\frac{1}{x})^2\ = \ 16-2\\\\\rightarrow (x)^2+(\frac{1}{x})^2 \ = \ 14$

$\ again \ square \ of \ the \given \ value :\\\\\rightarrow (x^2+(\frac{1}{x})^2 )^2\ = \ (14)^2\\\\\rightarrow (x^2)^2+((\frac{1}{x})^2 )^2+ 2.(x)^2.(\frac{1}{x})^2 = \ (14)^2\\\\\rightarrow (x)^4+(\frac{1}{x})^4 + 2= \ 196\\\\\rightarrow (x)^4+(\frac{1}{x})^4 = \ 196-2\\\\\rightarrow (x)^4+(\frac{1}{x})^4 = \ 194$

Learn more:

• Proving: https://brainly.in/question/7117106