Question

plz answer this Q7............

Answer 1

Hello,

Nice question......
We can solve this by using identities.

The identities to be used are:-
${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$
${x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

Now, first of all we have been given..
$a + b = 8 \\ {a}^{2} + {b}^{2} = 85$
Using 1st identity

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ {8}^{2} = 85 + 2ab \\ or \: \: 2ab = 64 - 85 = - 21 \\ ab = \frac{ - 21}{2} = - 10.5$

Now, using 2nd identity :-

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} ) \\ {a}^{3} + {b}^{3} = 8 \times (85 - ( \frac{ - 21}{2} ) \\ {a}^{3} + {b}^{3} \: = 8 \times \frac{191}{2} = 4 \times 191 = 764$

Hope this will be helping you ✌️ ✌️