4 variables

Algebra Level 3

If a + b + c + d = 37 a + b + c + d = 37 ,

b + c + d = 7 b + c + d = 7 ,

a + c = 3 a + c = 3 ,

b d − c 2 = 29 bd - c^{2} = 29 ,

Then find the value of a 2 + b 2 + c 2 + d 2 a^{2} +b^{2}+c^{2}+d^{2} .


The answer is 1269.

Vaibhav Priyadarshi by Vaibhav Priyadarshi , 17, India

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1 solution

Michael Mendrin
May 15, 2018

( a 2 + b 2 + c 2 + d 2 ) = ( a + b + c + d ) 2 − 2 ( b + c + d ) ( a + c ) − 2 ( b d − c 2 ) = 3 7 2 − 2 ⋅ ⋅ 3 − 2 ⋅ 29 = 1269 (a^2+b^2+c^2+d^2)= (a+b+c+d)^2-2(b+c+d)(a+c)-2(bd -c^2) = 37^2-2\cdot \cdot 3 -2\cdot 29 = 1269

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