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Verify: (a² - b²) (a² + b²) + (b² - c²) (b² + c²) + (c² - a²) + (c² + a²) = 0

Solution:

Given, (a² - b²) (a² + b²) + (b² - c²) (b² + c²) + (c² - a²) + (c² + a²) = 0

L.H.S = (a² - b²) (a² + b²) + (b² - c²) (b² + c²) + (c² - a²) + (c² + a²)

= [(a²)² - (b²)²] + [(b²)² - (c²)²] + (c² - a²) + (c² + a²)

= a⁴ - b⁴ + b⁴ - c⁴ + (c² - a²) + (c² + a²)

= a⁴ - c⁴ + (c² - a²) + (c² + a²)

= [(a²)² - (c²)²] + (c² - a²) + (c² + a²)

= (a² - c²) (a² + c²) + (a² + c²) + (c² - a²)

= (a² + c²) [(a² - c²) + 1] + (c² - a²)

≠ 0 ≠ R.H.S

L.H.S. ≠ R.H.S.

✦ Try This: Verify: (x³ + y³) (x³ - y³) +(y³ + z³) (y³ - z³)+(z³ + x³)(z³- x³) = 0

Given, (x³ + y³) (x³ - y³) +(y³ + z³) (y³ - z³)+(z³ + x³)(z³- x³) = 0

L.H.S = (x³ + y³) (x³ - y³) +(y³ + z³) (y³ - z³)+(z³ + x³)(z³- x³)

= [(x³)² - (y³)²] + [(y³)² - (z³)²] + [(z³)² - (x³)²]

= [x⁶ - y⁶] + [y⁶ - z⁶] + [z⁶ - x⁶]

= x⁶ - y⁶ + y⁶ - z⁶ + z⁶ - x⁶

= 0 = R.H.S

L.H.S. = R.H.S.

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

NCERT Exemplar Class 8 Maths Chapter 7 Problem 113(vii)

Summary:

(a² - b²) (a² + b²) + (b² - c²) (b² + c²) + (c² - a²) + (c² + a²) = 0 is not true

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