If x - (1/x) = 7 then find the value of x² + (1/x)².

Solution:

Given, x - (1/x) = 7

Using standard identity: (a - b)² = a² - 2ab + b²

[x - (1/x)]² = x² - 2(x)(1/x) + (1/x)²

[x - (1/x)]² = x² + (1/x)² - 2(x)(1/x)

[x - (1/x)]² + 2(x)(1/x) = x² + (1/x)²

[7]² + 2 = x² + (1/x)²

x² + (1/x)² = 49 + 2 = 51

✦ Try This: If x +(1/x) = 9 then find the value of x² + (1/x)² .

Given,x + (1/x) = 9

Using standard identity: (a + b)² = a² + 2ab + b²

[x + (1/x)]² = x² + 2(x)(1/x) + (1/x)²

[x + (1/x)]² = x² + (1/x)² + 2(x)(1/x)

[x + (1/x)]² - 2(x)(1/x) = x² + (1/x)²

[9]² - 2 = x² + (1/x)²

x² + (1/x)² = 81 - 2 = 79

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

NCERT Exemplar Class 8 Maths Chapter 7 Problem 117

If x - (1/x) = 7 then find the value of x² + (1/x)².

Summary:

If x - (1/x) = 7 then the value of x² + (1/x)² is 51

☛ Related Questions:

• Factorise x² + (1/x)² + 2 - 3x - (3/x)
• Factorise p⁴ + q⁴ + p²q²
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