Question

If a+b+c=14a2+b2+c2=100then,ab+bc+ca,is

Answer 1

Answer:

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Answer 2

Question:

$If \: a + b + c = 14, \: {a}^{2} + {b}^{2} + {c}^{2} = 100, then \: ab + bc + ca \: is?$

Answer:

$The \: value \: of \:\underline\bold{ab + bc + ca\:is \:48}$

Given data:

a + b + c = 14

a² + b² + c² = 100

To find:

To find the value of ab + bc + ca .

Step-by-step explanation:

We know that,( Formula )

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

It also can be written as,

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

$\longrightarrow {(14)}^{2} = (100) + 2(ab + bc + ca)$

$\longrightarrow 196 = (100) + 2(ab + bc + ca)$

$\longrightarrow 2(ab + bc + ca) = 196 - 100$

$\longrightarrow 2(ab + bc + ca) = 96$

$\longrightarrow \boxed{ab + bc + ca = 48}$

Verification:

${14}^{2} = 100 + 2(48)$

$196 = 100 + 96$

$196 = 196$

Hence verified.

Formula used:

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