Question

If a + b = 8 , a square + b square = 34 find a cube + b cube.​

Answer 1

Answer:

152

Taking the value of b as 8-a and then putting it in a2+b2=34

Answer 2

We have,
$a + b = 8$
and,
${a}^{2} + {b}^{2} = 34$


As we know,

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$


We already have all the values except for ab,
so solving for ab now,
${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} = {8}^{2} = 64$
subsituing the values for a and b squared,
$34 + 2ab = 64 \\ 2ab = 30 \\ ab = 15$


Now that we have all the values let's just substitute them for oyr final result,

$(8)(34 - 15) \\ = (8)(19) \\ = 152$


Therefore your answer is 152.