Question

If a+b+c= 8 and ab+ bc + ca=19
Find a square + b sq. + c sq

Answer 1

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Answer 2

Answer:

The value of the expression a² + b² + c² is 26.

Step-by-step explanation:

The expansion of (a + b + c)² is:

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

It is provided that:

a + b + c = 8

ab + bc + ca = 19.

Compute the value of a² + b² + c² as follows:

$(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca)\\8^{2}=a^{2}+b^{2}+c^{2}+(2\times19)\\64=a^{2}+b^{2}+c^{2}+38\\a^{2}+b^{2}+c^{2}=26$

Thus, the value of the expression a² + b² + c² is 26.