Question

If p+q+r=12 and p^2 +q^2+r^2=50, find pq+ qr +pr.

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Answer 1

Explanation:

$\sf \blue{Given:}$

• p + q + r = 12
• p² + q² + r² = 50

$\sf \red{To \: Find:-}$

• pq + qr + pr

$\sf\pink{Understanding:-}$

• In this question,
• we have given two different values which are p+q+r = 12 and p²+q²+r² = 50 and asked to find out value of pq+qr+pr. To solve these types of questions, we need some algebraic expressions which help us solve these easily.

$\sf \orange{Solution:}$

• As we have mentioned above that we need algebraic expressions to solve,

$\sf \purple{We \: know \: that:-}$

$\large{\boxed{\red{\small{\bf{(a+b+c)^2~=~a^2+b^2+c^2+2(ab+bc+ca)}}}}} </p><p>$

$\sf \blue{Where:-}$

• p = a
• q = b
• r = c

$\bf \pink{Let's \: put \: value \: in \: formula \: :-}$

(p+q+r)² = p² + q² + r² +2(pq + qr + rs)

→ 12² = 50 + 2(pq + qr + pr)

→ 144 = 50 + 2(pq + qr + pr)

→ 144 - 50 = 2(pq + qr + pr)

→ 94 = 2(pq + qr + pr)

→ pq + qr + pr = 94/2

→ pq + qr + pr = 47

$\sf\green {Therefore,}$

$\large{\boxed{\purple{\small{\bf{value~of~pq+qr+ pr~=~47}}}}}$

$\sf \gray{value of pq+qr+pr = 47}$

$\sf \underline{More \: algebraic \: identities \: related \: to \: this:-}$

(a+b)² = a² + b² + 2ab

(a-b)² = a² + b² - 2ab

(a+b)(a-b) = a² - b²

(a + b + c)² = a^2+b^2+c^2+2(ab+bc+ca)

(a+b)³ = a³ + b³ + 3ab(a+b)

(a-b)³ = a³ - b³ - 3ab(a-b)

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Answer 2

Explanation:

Explanation:

$\sf \blue{Given:}$

• p + q + r = 12
• p² + q² + r² = 50

$\sf \red{To \: Find:-}$

• pq + qr + pr

$\sf\pink{Understanding:-}$

• In this question,
• we have given two different values which are p+q+r = 12 and p²+q²+r² = 50 and asked to find out value of pq+qr+pr. To solve these types of questions, we need some algebraic expressions which help us solve these easily.

$\sf \orange{Solution:}$

• As we have mentioned above that we need algebraic expressions to solve,

$\sf \purple{We \: know \: that:-}$

$\large{\boxed{\red{\small{\bf{(a+b+c)^2~=~a^2+b^2+c^2+2(ab+bc+ca)}}}}}$

$\sf \blue{Where:-}$

• p = a
• q = b
• r = c

$\bf \pink{Let's \: put \: value \: in \: formula \: :-}Let$

$\pink{ sputvalueinformula:−}$

(p+q+r)² = p² + q² + r² +2(pq + qr + rs)

→ 12² = 50 + 2(pq + qr + pr)

→ 144 = 50 + 2(pq + qr + pr)

→ 144 - 50 = 2(pq + qr + pr)

→ 94 = 2(pq + qr + pr)

→ pq + qr + pr = 94/2

→ pq + qr + pr = 47

$\sf\green {Therefore,}$

$\large{\boxed{\purple{\small{\bf{value~of~pq+qr+ pr~=~47}}}}}$

$\sf \gray{value of pq+qr+pr = 47}$

$\sf \underline{More \: algebraic \: identities \: related \: to \: this:-}$

(a+b)² = a² + b² + 2ab

(a-b)² = a² + b² - 2ab

(a+b)(a-b) = a² - b²

(a + b + c)² = a^2+b^2+c^2+2(ab+bc+ca)

(a+b)³ = a³ + b³ + 3ab(a+b)

(a-b)³ = a³ - b³ - 3ab(a-b)

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