Solve the Equation (bonus question)(free rating)

Algebra Level 2

The sum of 3 numbers is 9.

If we multiply third number by 3 and add to the second number, we get 16.

By adding the first and the third number and then subtracting twice the second number from this sum,we get 6

Find the value of ( x y + y z + z x ) ( x y z ) ( x 2 + y 2 + z 2 ) (xy+yz+zx)(xyz)(x^2+y^2+z^2)


The answer is 12075.

Anirudha Nayak by Anirudha Nayak , 24, India

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2 solutions

Asad Jawaid
Oct 12, 2015

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Hello,peace be upon you,

as for this, 1st no. = x, 2nd no. = y , 3rd no. = z ,

x+y+z = 9 (2nd),

3z+y = 16

x+z-2y =6 --------> x+z = 6 + 2y (1st)

substitute (1st) into (2nd),

6 + 3y = 9

y = 1

z = (16 - 1) / 3 = 5

x = 9 - 5 - 1 = 3,

as x = 3 , y = 1, z = 5,

therefore, the final answer is (3+5+15)(15)(9+1+25) = 12 075,

thanks...

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice Solution!

Asad Jawaid - 5 years, 5 months ago

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