Question

if x+1/7=root7,find the value of x^4+1/x^4​

Answer 1

Given:
x + 1/x = √7
To find out:
Find the value of x² + 1/x² ?
Solution:
We know that,
( a + b ) ² = a² + b² + 2ab
x + 1/x = √7
☆ Squaring both sides,we get
( x + 1/x )² = ( √7 )²
⇒ x² + 1/x² + 2 = 7
⇒ x² + 1/x² = 7 - 2
⇒ x² + 1/x² = 5
Hence, the value x² + 1/x² is 5 .
More identities
1.(a+b)²= a²+ b²+2ab
2.(a-b)²= a²-2ab +b²
3.(a+b)(a-b)= a²-b²
4.( a+b+c) = a+b+c+2ab+2ba+2ca
5. ( a + b )³ = a³ + b³ - 3ab( a + b