Question

If x + 1/x = 3 find the value of x4 1/x4.​

Answer 1

Answer:

take square of x+1/x = square of 3 , now x2+1/x2+2 = 9 , now x2+1/x2 = 9-2 , x2+1/x2= 7 , now take whole square of x2+1/x2 = square of 7 , x4+1/x4+2 = 49 , now x4+1/x4= 49-2 , x4+1/x4=47 if ans is correct brainlist my ans and connect to me and give me 5 stars

Answer 2

Answer:

47

Step-by-step explanation:

Given Question:

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

To find:

${x}^{4} + \frac{1}{ {x}^{4} } \\ = {x}^{4} + ( \frac{1}{x} ) {}^{4} \\ = { ({x}^{2}) }^{2} + {(( \frac{1}{x} ) {}^{2} )}^{2} \\ = (x {}^{2} + ( \frac{1}{x} ) {}^{2} ) {}^{2} - 2 \times {x}^{2} \times {\frac{1}{x {}^{2} } } \\ = (x {}^{2} + ( \frac{1}{x} ) {}^{2} ) {}^{2} - 2 \\ = ((x + \frac{1}{x} ) {}^{2} - 2 \times x \times \frac{1}{x} ) {}^{2} - 2 \\ = ((x + \frac{1}{x} ) {}^{2} - 2 ) {}^{2} - 2$

Thus, by placing the values,

$({3}^{2} - 2) {}^{2} - 2 \\ = {(9 - 2)}^{2} - 2 \\ = 7 {}^{2} - 2 \\ = 49 - 2 \\ = 47 \: \: (ans.)$

Hope this helps you. ^_^