If x + 1 x = 9 , then find the value of x 2 + 1 x 2 and x 4 + 1 x 4 .

Given, x + 1 x = 9 We know that a + b 2 = a 2 + 2 a b + b 2 . ∴ x 2 + 1 x 2 + 2 × x × 1 x = x + 1 x 2 ⇒ x 2 + 1 x 2 + 2 = 9 2 ⇒ x 2 + 1 x 2 + 2 = 81 ⇒ x 2 + 1 x 2 = 81 - 2 ⇒ x 2 + 1 x 2 = 79 ________ 1 Again, x 2 2 + 1 x 2 2 + 2 × x 2 × 1 x 2 = x 2 + 1 x 2 2 ⇒ x 4 + 1 x 4 + 2 = 79 2 [From 1 ] ⇒ x 4 + 1 x 4 + 2 = 6241 ⇒ x 4 + 1 x 4 = 6241 - 2 ⇒ x 4 + 1 x 4 = 6239 Hence, x 4 + 1 x 4 = 6239

E M B I B E

New Global Mathematics - 7>Chapter 6 - Algebraic Expressions>EXERCISE 6.5

Dr Pooranmal and Ashfaq A Khan Solutions for Chapter: Algebraic Expressions, Exercise 5: EXERCISE 6.5

Author:Dr Pooranmal & Ashfaq A Khan

Dr Pooranmal Mathematics Solutions for Exercise - Dr Pooranmal and Ashfaq A Khan Solutions for Chapter: Algebraic Expressions, Exercise 5: EXERCISE 6.5

Attempt the practice questions on Chapter 6: Algebraic Expressions, Exercise 5: EXERCISE 6.5 with hints and solutions to strengthen your understanding. New Global Mathematics - 7 solutions are prepared by Experienced Embibe Experts.