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Types of Expressions Based on the Number of Terms

Find : a2+b2...

Question

Find : $a^{2} + b^{2} + c^{2}$ , if $a + b + c = 9$ and $a b + b c + c a = 24$

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Solution

Formula ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$
Substituting $a + b + c = 9; a b + b c + c a = 24$
$9^{2} = a^{2} + b^{2} + c^{2} + 2 (24)$
$81 - 48 = a^{2} + b^{2} + c^{2}$
$a^{2} + b^{2} + c^{2} = 33$

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Q. If a + b + c = 9 and ab + bc + ca = 40, find a² + b² +c².

Q. If a² + b² + c² = 24 and ab + bc + ca = – 4, then a + b + c = ________.

Q. Question 30
if

a + b + c = 9

a b + b c + c a = 26

a^{2} + b^{2} + c^{2}

If $a + b + c = 9$ and $a b + b c + c a = 40$ . Find the value of $a^{2} + b^{2} + c^{2}$ .

Q. If a² + b² + c² + ab + bc + ca = 89 and (a + b) : (b + c) : (c + a) = 12 : 5 : 3, where a, b and c are real numbers, then (a² + b² + c² – ab – bc – ca) equals

यदि a² + b² + c² + ab + bc + ca = 89 तथा (a + b) : (b + c) : (c + a) = 12 : 5 : 3, जहाँ a, b व c वास्तविक संख्याएँ हैं, तब (a² + b² + c² – ab – bc – ca) बराबर है

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