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a-b=3 ,b-c=5 then find a^2+b^2 + …

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a-b=3 ,b-c=5 then find a^2+b^2 + c^2 -ab-bc-ca

Posted by Sambhaji Thakur 6 years, 7 months ago

CBSE > Class 12 > Mathematics

1 answers

Shubham Aggarwal 6 years, 7 months ago

a-b=3 Sq. Both sides (a-b)^2=9 a^2+b^2-2ab=9--------------(i) b-c=5 Sq. Both sides (b-c)^2=25 b^2+c^2-2bc=25-----------(ii) Now, adding a-b=3 & b-c=5 We get, a-c=8 Sq. Both sides (a-c)^2=64 a^2+c^2-2ac=64--------------(iii) Now, adding eq (i) (ii) (iii) We get 2a^2+2b^2+2c^2-2ab-2bc-2ca=98 Taking 2 common from L.H.S 2(a^2+b^2+c^2-ab-bc-ca)=98 Dividing by 2 both sides we get, a^2+b^2+c^2-ab-bc-ca=49

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