Question

find P cube minus Q cube if P minus Q is equal to minus 8, PQ is equal to minus 12​

Answer 1

Answer:

The value of P³ - Q³ is -224.

Step-by-step explanation:

It is provided that:

$P-Q=-8\\PQ=-12$

The formula of (a + b)² and (a - b)² are:

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

Use these relations to compute the value of P and Q as follows:

Step 1: Compute the value of P² + Q² as follows:

$(P-Q)^{2}=P^{2}+Q^{2}-2PQ\\(-8)^{2}=P^{2}+Q^{2}-(2\times-12)\\64=P^{2}+Q^{2}+24\\P^{2}+Q^{2}=40$

Step 2: Compute the value of P + Q as follows:

$(P+Q)^{2}=P^{2}+Q^{2}+2PQ\\=40+(2\times-12)\\=40-24\\=16\\P+Q=4$

Step 3: Add the  equations P - Q = -8 and P + Q = 4 as follows;

$P + Q = 4\\P - Q = -8\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2P=-4\\P=-2$

Step 4: Use the value of P = - 2 in the  equation P + Q = 4 and solve for Q as follows:

$P+Q=4\\-2+Q=4\\Q=6$

Step 5: Compute the value of P³ - Q³ as follows:

$P^{3} -Q^{3}=(-2)^{3}-(6)^{3}=-8-216=-224$

Hence the value of P³ - Q³ is -224.

Answer 2

Answer:

the answer is 667 okay bcoz p and q are not the symbols but they use in maths calculations