Question

7. a+b+c= 9 and ab+bc+ca=26.Find
${a}^{2} + {b}^{2} + {c}^{2}$


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Answer 1

We know the formula:

(a+b+c)² = a² + b² + c² + 2(ab+bc+ca)

Given:

a+b+c = 9 & ab+bc+ca = 26

Now putting the values in the above formula,

We get,

(9)² = a² + b² + c² + 2×26

81 = (a² +b² +c²) + 52

(a² +b²+c²) = 81-52

(a² + b² + c²) = 29

Answer 2

Answer:

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Given that a + b + c = 9

and ab + bc + ca = 26.

So, ${a}^2 +{b}^2+{c}^2$ =?.

We know that ${a+b+c}^2$ = ${a}^2 +{b}^2+{c}^2$ +2( + bc + ca)

a + b + c = 9.

squaring both sides we get =

${a}^2 +{b}^2+{c}^2$ +2( + bc + ca) =9×9

or ${a}^2 +{b}^2+{c}^2$ +2 × 26 =81.

or ${a}^2 +{b}^2+{c}^2$ = 81-52.

Therefore, ${a}^2 +{b}^2+{c}^2$ =29