{ (0.52)³ + (0.62)³ - (0.14)³ + 3 (0.52) (0.62) (0.14) } / [ (0.52)² + (0.62)² + (0.14)² - (0.52) (0.62) + (0.62) (0.14) + (0.52) (0.14) ] = 1

Open in App

Solution

$To prove : - \frac{{(0.52)}^{3} + {(0.62)}^{3} - {(0.14)}^{3} + 3 (0.52) (0.62) (0.14)}{{(0.52)}^{2} + {(0.62)}^{2} + {(0.14)}^{2} - (0.52) (0.62) + (0.62) (0.14) + (0.52) (0.14)} = 1 We know, x^{3} + y^{3} + z^{3} - 3 xyz = (x + y + z) (x^{2} + y^{2} + z^{2} - xy - yz - xz) so, \frac{x^{3} + y^{3} + z^{3} - 3 xyz}{(x + y + z) (x^{2} + y^{2} + z^{2} - xy - yz - xz)} = 1 Here, x = 0.52, y = 0.62 and z = - 0.14 therefore, \frac{{(0.52)}^{3} + {(0.62)}^{3} - {(0.14)}^{3} + 3 (0.52) (0.62) (0.14)}{{(0.52)}^{2} + {(0.62)}^{2} + {(0.14)}^{2} - (0.52) (0.62) + (0.62) (0.14) + (0.52) (0.14)} = 1 Hence Proved .$

Suggest Corrections

Similar questions

\frac{0.86 \times 0.86 \times 0.86 + 0.14 \times 0.14 \times 0.14}{0.86 \times 0.86 - 0.86 - 0.14 + 0.14 \times 0.14}

\frac{0.46 \times 0.46 + 2 \times 0.46 \times 0.14 + 0.14 \times 0.14}{0.46 \times 0.46 - 0.14 \times 0.14}

? - (0.6)^{2} = (0.7)^{2} \div 0.35

The value of ${0.6}^{2}$ is

\frac{1.25 \times 1.25 - 0.87 \times 0.87}{1 - 0.62}

Join BYJU'S Learning Program