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if a+b+c=5 and ab+bc+ca =10 then prove that a3 +b3 +c3-3abc =-25

Posted by Param Makvana 4 years, 8 months ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 4 years, 8 months ago

we know ,

a³ + b³ + c³ -3abc = (a + b + c )(a² + b² + c² -ab -bc-ca)

now ,

a + b + c = 5
ab + bc + ca = 10

(a + b + c)² = a² + b² + c² +2(ab + bc+ca)
(5)² -2×10 = a² + b² + c²
a² + b² + c² =5

hence ,

a³ + b³ +c³ -3abc = ( a + b + c )(a² + b² + c² -ab- bc-ca)

=( 5)( 5 - 10) = 5 × (-5) = -25

hence proved

0Thank You

ANSWER

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CBSE > Class 09 > Mathematics