Question

If a+b+c= 12 and a? + b2 + 2 = 64, find the value of ab + bc + ac.

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Answer 1

=> ab + bc + ca = 40

Step-by-step explanation:

=> a + b + c = 12

=> squaring both sides :-

=> (a + b + c)² = (12)²

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

=> a² + b² + c² + 2(ab + bc + ca) = 144

• a² + b² + c² = 64

=> 64 + 2(ab + bc + ca) = 144

=> 2(ab + bc + ca ) = 80

=> ab + bc + ca = 80/2

=> ab + bc + ca = 40

Answer 2

${ \huge{ \pink{ \underline{ \rm{Given}} \colon}}}$

${ \large{➺ \: \: \bf{a + b + c = 12}}}$

${ \large{➺ \: \: \bf{a {}^{2} + b {}^{2} + c {}^{2} = 64 }}}$

${ \huge{ \green{ \underline{ \rm{To \: \: find}} \colon}}}$

${ \large{➢ \: \: \bf{Value \: \: of \: \: (ab + bc + ca)}}}$

${ \large{ \red{ ➻ \: \: \boxed{ \tt{(a + b + c) {}^{2} = a {}^{2} + b {}^{2} + c {}^{2} + 2(ab + bc + ca)}}}}}$

${ \large{➾ \: \: \bf{12 {}^{2} = 64 + 2(ab + bc + ca)}}}$

${ \large{➾ \: \: \bf{ \dfrac{144 - 64}{2} = ab + bc + ca}}}$

${ \large{➾ \: \: \bf{ab + bc + ca ={ \cancel{ \dfrac{80}{2} {} }}}}}$

${ \large{ { { \rm{ \blue{ \therefore{\underline{\overline{ \boxed{ \rm{ab + bc + ca = 40}} }}\: \:Ans.}}}}}}}$