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प्रश्न
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
पर्याय
35
58
127
none of these
उत्तर
We have to find `a^2 + b^2 + c^2`
Given `a+b + c = 9,ab+bc +ca = 23`
Using identity `(a+b+c)^2 = a^2 + b^2 +c^2+2ab + 2bc + 2ca` we get,
`(9)^2 = a^2 +b^2 + c^2+ 2 (ab + bc + ca)`
` 9 xx 9 = a^2 + b^2 + c^2 +2 xx 23`
`81 = a^2 + b^2 + c^2+46`
By transposing +46 to left hand side we get,
`81 - 46 = a^2 +b^2 +c^2`
` 35 = a^2 +b^2 +c^2`
Hence the value of `a^2 +b^2 +c^2` is 35.
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