By using the suitable identities evaluate x² + 1/x², If x + (1/x) = 5

Solution:

Given that, x + (1/x) = 5

Squaring on both sides we get,

[x + (1/x)]² = 25

Now using the identity: (a + b)² = a² + 2ab + b²,

Here, a = x and b = 1/x

x² + (2 × x × (1/x)) + (1/x)² = 25

x² + 2 + 1/x² = 25

x² + 1/x² = 25 - 2

x² + 1/x² = 23

✦ Try This: By using suitable identities evaluate, x³ + 1/x³, If x + 1/ x = 7

Given that, x + 1/ x = 7

Cube on both sides we get,

[x + 1/x]³ = 7³

Now using the identity (a + b)³ = a³ + b³ + 3ab (a + b)

Here, a = x and b = 1/x

x³ + 1/x³ + 3(x)(1/x)(x + 1/x) = 343

x³ + 1/x³ +3(1)(7) = 343

∴x³ + 1/x³ = 322

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Sample Problem18

Summary:

Evaluating x² + 1/x², given x + (1/x) = 5 we get, x² + 1/x² = 23

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