Question

If x-y =7and x² +y²=85 find the value of x³-y cube​

Answer 1

Answer:

${x}^{3} - {y}^{3} = 721$

Explanation:

Given:

$x - y = 7 \: .............(i)$

${x}^{2} + {y}^{2} = 85 \: .............(ii)$

To FInd:

${x}^{3} - {y}^{3}$

Steps:

We know that,

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + {y}^{2} + xy) \: .............(iii)$

Squaring equation (i), we get:

${x}^{2} + {y}^{2} - 2xy = 49 \: .............(iv)$

Subtracting equation (ii) from (iv), we get

${x}^{2} + {y}^{2} - 2xy - {x}^{2} - {y}^{2} = 49 - 85$

$- 2xy = - 36$

$xy = 18$

We have,

$(x - y ) = 7$

${x}^{2} + {y}^{2} = 85$

$xy = 18$

So, we put the values of these three in equation (iii), we get:

${x}^{3} - {y}^{3} = 7 \times (85 + 18)$

${x}^{3} - {y}^{3} = 7 \times 103$

${x}^{3} - {y}^{3} = 721$

Therefore, the answer is 721.