Math, asked by itzcutemahira, 10 months ago

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

Answers

Answered by sweetanalyise
129

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

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

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

  • ab + bc + ac = ?

\small{\underline{\sf{\blue{Formula\:Used:\rightarrow}}}}

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

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

\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.

Answered by SaI20065
3

A+b+c=10

Squaring both both

(a+b+c)²=(10)²

=>a^2+b^2+c^2+2ab+2bc+2ca = 100

30+2(ab+bc+ca) =100}

=>2(ab+bc+ca)=100-30=70

=>ab+bc+ca=70/2=35

=>ab+bc+ca=35

Similar questions