Question

If p+q+r=7 and p(2)+q(2) +r(2) = 11 find pq+qr+rp​

Answer 1

SOLUTION

GIVEN

$\sf{}p + q + r = 7 \: \: and \:$

$\sf{} {p}^{2} + {q}^{2} + {r}^{2} = 11$

TO DETERMINE

The value of pq + qr + rp

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

$\sf{} {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)$

EVALUATION

Here it is given that

$\sf{}p + q + r = 7 \: \: and \:$

$\sf{} {p}^{2} + {q}^{2} + {r}^{2} = 11$

Now

$\sf{} {(p + q + r)}^{2} = {p}^{2} + {q}^{2} + {r}^{2} + 2(pq + qr + rp)$

$\implies\sf{} {(7)}^{2} = 11 + 2(pq + qr + rp)$

$\implies\sf{} 49 = 11 + 2(pq + qr + rp)$

$\implies\sf{} 49 - 11 = 2(pq + qr + rp)$

$\implies\sf{} 38 = 2(pq + qr + rp)$

$\implies\sf{} 2(pq + qr + rp) = 38$

$\implies\sf{} pq + qr + rp = 19$

FINAL ANSWER

$\boxed{ \: \: \sf{} pq + qr + rp = 19 \: \: }$

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Answer 2

Answer

given:

p+q+r=7

p(2)+q(2)+r(2)=11

pq+qr+pr=??

formula:

(a+b+c)*2=a(2)+b(2)+c(2)+2(ab+bc+ac)

solution:

(p+q+r)*2=p(2)+q(2)+r(2) + 2(pq+qr+pr)

(7)*2 = 11 + 2(pq+qr+pr)

49= 11 + 2(pq+qr+pr)

49-11 = 2(pq+qr+pr)

38 = 2(pq+qr+pr)

=(pq+qr+pr) = 19

Step-by-step explanation: