L 3 /m 3 + m 3 / n 3 + n 3 /l 3 - 3 Factorise
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Solution:-
a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ca)
Here,
a = l/m, b= m/n and c = n/l
Thus,
l³/m³ + m³/n³ + n³/l³ -3*l/m*m/n*n/l = [l/m + m/n +n/l][l²/m² + m²/n² + n²/l² - l/m*m/n - m/n*n/l - n/l*l/m
l³/m³ + m³/n³ + n³/l³ - 3 = [l/m + m/n + n/l][l²/m² + m²/n² + n²/l² - l/n - m/l - n/m]
Answer.
a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ca)
Here,
a = l/m, b= m/n and c = n/l
Thus,
l³/m³ + m³/n³ + n³/l³ -3*l/m*m/n*n/l = [l/m + m/n +n/l][l²/m² + m²/n² + n²/l² - l/m*m/n - m/n*n/l - n/l*l/m
l³/m³ + m³/n³ + n³/l³ - 3 = [l/m + m/n + n/l][l²/m² + m²/n² + n²/l² - l/n - m/l - n/m]
Answer.
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