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 = ?

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

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

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

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

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

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

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

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

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

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

➱The value of ab + bc + ac = 35.

Answer 2

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

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.