Question

If the number p is 7 more than the number q and the sum of the square of p and q is 85, find the product of p and q.

Answer 1

Answer:

The product of p and q is 18.

Step-by-step explanation:

Given

The numbers are p and q

To find the product of p and q

Solution:

According to question

$p+7=q...Eq.1$

$(p+q)^{2} =85...Eq. 2$

$From Eq.1\\p+7=q\\p=q-7\\\\From Eq. 2\\p^{2} +q^{2} =85\\Putting the value of p in Eq.2\\(q-7)^{2} +q^{2} =85\\or, q^{2}-14q+49+q^{2} =85\\ or, 2q^{2} -14q =85-49\\or, 2q^{2} -14q-36=0\\or, 2(q^{2} -7q-18)=0\\or, q^{2} -7q-18=0\\or, q^{2} -(9-2)q-18=0\\\or, q^{2} -9q+2q-18=0\\\or,q(q-9)+2(q-9)=0\\or, (q+2)(q-9)=0\\either, q+2=0\\q= -2\\or, q-9=0\\q=9\\Again\\From Eq.1\\when q= -2, p=q-7= -2-7=-9\\when q=9. p=q-7=9-7=2$

Hence, a product of p and q is 18.

Answer 2

Answer:

The correct answer that is the product of p and q will be 18.

Step-by-step explanation:

Given that:

Two numbers are given that is p and q.

Also, p is 7 more than the q it means;

equation1:

$p + 7 = q$

and sum of square of the two given number is 85, it means;

equation2:

$(p + q)^{2} = 85$

Finding the value of p and q:

putting the value of q from equation 1 into equation 2, we get;

$(p + p + 7)^{2} = 85$

By solving, we get;

$(2p + 7)^{2} = 85$

By solving further we get;

p=-9 or 2

now putting value of p in equation 1, we get;

q= -2 or 9 respectively

therefore p*q will be:

$- 9 \times - 2 = 18$

or,

$2 \times 9 = 18$

The product of p and q will be 18.