Question

Q21. If a3 + b3 = 125 and a - b = 5 then a² + ab + b² is:​

Answer 1

Question

If a³ -b³= 125 and a - b = 5 then a² + ab + b² is:

Given

• a³ - ³= 125
• a-b=5

To find

• a²+b²+ab

${\boxed{ \gray{ \sf{Formula \: used = {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + {b}^{2} + ab)}}}}$

step by the Explanation

$\tt{\dashrightarrow a³-b³=(a-b)(a²+b²+ab)}$

$\tt{\dashrightarrow 125= 5(a²+b²+ab)}$

$\tt{\dashrightarrow a²+b²+ab= \frac{125}{5}}$

$\tt{\dashrightarrow a²+b²+ab=\bf{\blue{ 25}}}$

$\\ \\ \sf{ for\ more\ information}$

$\sf{(a + b) ^{3} = {a}^{3} + b^{3} + 3ab(a + b)}$

$\sf{(a - b) ^{3} = {a}^{3} - b^{3} - 3ab(a - b)}$

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

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

Answer 2

$\sf \pmb{Answer :}$

Question

If a³ -b³= 125 and a - b = 5 then a² + ab + b² is:

Given

a³ - ³= 125

a-b=5

To find

a²+b²+ab

${\boxed{ \gray{ \sf{Formula \: used = {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + {b}^{2} + ab)}}}}$

step by the Explanation

$\tt{\dashrightarrow a³-b³=(a-b)(a²+b²+ab)}$

$\tt{\dashrightarrow 125= 5(a²+b²+ab)}$

$\tt{\dashrightarrow a²+b²+ab= \frac{125}{5}}$

$\tt{\dashrightarrow a²+b²+ab=\bf{\blue{ 25}}}$

$\\ \\ \sf{ for\ more\ information}$

$\sf{(a + b) ^{3} = {a}^{3} + b^{3} + 3ab(a + b)}$

$\sf{(a - b) ^{3} = {a}^{3} - b^{3} - 3ab(a - b)}$

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

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