Question

Find the value of 27a3+64 b3 if 3a+4b=10 and ab=2

Answer 1

➭ Answer :-

• 27a³ + 64b³ = 280

step by step explaination :

➭ To find :-

• the value of 27a³ + 64b³

➭ Solution :-

$\sf 3a + 4b = 10$

Cube on both sides

$\longrightarrow \sf (3a + 4b) {}^{3} = 10$

$\longrightarrow \sf {(3a)}^{3} + {(4b)}^{3} + 3 \times 3a \times 4b(3a + 4b = 1000$

$\longrightarrow \sf 27 {a}^{3} + 64 {b}^{3} + 36ab(3a + 4b) = 1000$

$\longrightarrow \sf 27 {a}^{3} + 64 {b}^{3} + 36 \times 2 \times 10 = 1000$

$\longrightarrow \sf 27 {a}^{3} + 64 {b}^{3} + 720 = 1000$

$\longrightarrow \sf 27 {a}^{3} + 64 {b}^{3} = 1000 - 720$

$\longrightarrow \sf 27 {a}^{3} + 64 {b}^{3} = 280$

Hence, 27a³ + 64b³ = 280.