Question

(a²+b²)(a + b)/(b-c)(c-a) - (b+c)(b²+c²)/(a-c)(a-b) - (c+a)(c²+a²)/(b-a)(b-c)​

Answer 1

Answer:

$\large\sf{\red{Answer\: :-}}$

$Given,  a {}^{2} +b {}^{2} +c {}^{2} =1$

$We \: know \: that, (a+b+c) {}^{2} ≥0$

$⇒a {}^{2} +b {}^{2} +c {}^{2} +2(ab+bc+ca)≥0$

$⇒1+2(ab+bc+ca)≥0$

$⇒ab+bc+ca≥ \frac{ - 1}{2}$

$Again, (b−c) {}^{2} +(c−a) {}^{2} +(a−b) {}^{2} ≥0$

$⇒2(a {}^{2} +b {}^{2} +c {}^{2} )−2(ab+bc+ca)≥0$

$⇒ab+bc+ca≤a {}^{2} +b {}^{2} +c {}^{2}$

$⇒ab+bc+ca≤1$

$Hence,  \frac{ - 1}{2} ≤ab+bc+ca≤1$

Answer 2

Sir Isaac Newton PRS was an English mathematician, physicist, astronomer, alchemist, theologian, and author widely recognised as one of the greatest mathematicians and physicists of all time and among the most influential scientists. He was a key figure in the philosophical revolution known as the Enlightenment.

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