Question

4. If p-2q = 6 and pq = 8, find the value of p^3-8q^3​

Answer 1

We have,

$p - 2q = 6$

Squaring Both Sides,

${p}^{2} + 4 {q}^{2} - 2pq = 36 \\ {p}^{2} + 4 {q}^{2} - 2(8) = 36 \\ {p}^{2} + 4 {q}^{2} = 36 + 16 = 52$

To Find:

${p}^{3} - 8 {q}^{3}$

By Using Identity,

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

So, We get

${p}^{3} - {(2q)}^{3} \\ = ( p - 2q)( {p}^{2} + 4 {q}^{2} + 2pq)$

Putting the values, We obtain

$= (6)(52 + 2 \times 18) \\ = (6)(88) = 528$