Question

if a²+b²+c²=30,a+b+c=10 then value of a +bc+ac​

Answer 1

$\small{\underline{\sf{\pink{Given:}}}}$

a² + b² + c² = 30.

a + b + c = 10.

$\small{\underline{\sf{\green{To\:Find:}}}}$

ab + bc + ac = ?

$\small{\underline{\sf{\blue{Formula\:Used:arrow}}}}$

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

$\small{\underline{\sf{\red{Solution:}}}}$

$\implies{{(10)}^{2} = 30 + 2ab+ 2bc + 2ca}$

$\implies{100 = 30 + 2(ab + bc + ca)}$

$\implies{100 - 30 = 2(ab + bc + ca)}$

$\implies{70 = 2(ab + bc + ac)}$

$\implies{2(ab + bc + ac) = 70}$

$\implies{ab + bc + ac = \frac{70}{2} }$

$\implies{ab + bc + ac = 35}$

➱The value of ab + bc + ac = 35.

$\huge\underline\bold\pink{Thanks}$

Answer 2

Correct Question :

›»› If a² + b² + c² = 30, a + b + c = 10 then find the value of ab + bc + ac

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Answer :

›»› The value of ab + bc + ac = 35

Given :

• a² + b² + c² = 30
• a + b + c = 10

To Find :

• The value of ab + bc + ac = ?

Required Solution :

As we know that

⇛ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

It is given that (a + b + c)² is 10 and a² + b² + c² is 30$.$

So ,

⇛ (10)² = 30 + 2ab + abc + 2ca

⇛ 10 × 10 = 30 + 2ab + abc + 2ca

⇛ 100 = 30 + 2ab + 2bc + 2ca

⇛ 100 = 3 + 2(ab + bc + ca)

⇛ 100 - 3 = 2(ab + bc + ca)

⇛ 70 = 2(ab + bc + ca)

⇛ 70/2 = ab + bc + ca

⇛ 35 = ab + bc + ca

⇛ ab + bc + ca = 35

║Hence, the value of ab + bc + ca is 35.║