Question

p²+p² = 5 and pq =2, find p³-q³​

Answer 1

$\sf{(p - q) = {p}^{2} + {q}^{2} - 2pq = 5 - 2(2) = 1 }$

$\sf{(p - q) = \sqrt{1 } = ±1 }$

$\sf{take} \: \frak{ 1}$

$\sf{ {p}^{3} - {q}^{3} = (p = q {)}^{3} - 3pq(p - q) = 1 - 3(2)(1) = - 5}$

$\sf{now} \: \frak{ - 1}$

$\sf{ {p}^{3} - {q}^{3} = 5}$

Hence the answer is 5.

Answer 2

$\\ \sf{(p - q) = {p}^{2} + {q}^{2} - 2pq = 5 - 2(2) = 1 }(p−q)=p </p><p>2</p><p> +q </p><p>2</p><p> −2pq=5−2(2)=1</p><p></p><p> \\ \sf{(p - q) = \sqrt{1 } = ±1 }(p−q)= </p><p>1</p><p> </p><p> =±1</p><p></p><p> \\ \sf{take} \: \frak{ 1}</p><p></p><p> \\ \sf{ {p}^{3} - {q}^{3} = (p = q {)}^{3} - 3pq(p - q) = 1 - 3(2)(1) = - 5}p </p><p>3</p><p> −q </p><p>3</p><p> =(p=q) </p><p>3</p><p> −3pq(p−q)=1−3(2)(1)=−5</p><p></p><p> \\ \sf{now} \: \frak{ - 1}</p><p></p><p> \\ \sf{ {p}^{3} - {q}^{3} = 5}p </p><p>3</p><p> −q </p><p>3</p><p> =5</p><p></p><p> \\ Hence \: the \: answe r \: is \: 5.$