Question

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

Answer 1

CORRECT QUESTION :–

• If a²+b²+c² = 30 , a+b+c = 10 then value of ab + bc + ac = ?

ANSWER :–

GIVEN :–

• a²+b²+c² = 30

• a + b + c = 10

TO FIND :–

• ab + bc + ac = ?

SOLUTION :–

• We know that –

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

• Put the values –

=> (10)² = 30 + 2ab + 2bc + 2ca

=> 100 = 30 + 2(ab + bc + ac)

=> 100 - 30 = 2(ab + bc + ac)

=> 70 = 2(ab + bc + ac)

=> 2(ab + bc + ac) = 70

=> ab + bc + ac = 70/2

=> ab + bc + ac = 35

• Hence , The value of ab + bc + ac = 35 .

Answer 2

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{Correct \:Question }}}}⋆$

If a² + b² + c² = 30, a + b + c = 10 then value of ab + bc + ac?

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{ANSWER}}}}⋆$

• ab + bc + ac = 35

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{EXPLANATION}}}}⋆$

$\blue{\bold{\underline{\underline{Given}}}}$

• a² + b² + c² = 30.
• a + b + c = 10.

$\blue{\bold{\underline{\underline{To \: Find}}}}$

• ab + bc + ac = ?

$\blue{\bold{\underline{\underline{Formula}}}}$

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

$\blue{\bold{\underline{\underline{Now}}}} </p><p>$

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

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

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

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

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

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

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

$\blue{\bold{\underline{\underline{ANSWER}}}}$

• The value of ab + bc + ac = 35.