Fraction of the Year
x + 2 1 + x + 0 7 + x + 1 − 5 + x + 8 3 = 0 Find ∣ x ∣ if x is real.
The answer is 3.5.
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1 solution
It will be easier if you add it up like this ( x + 2 1 + x + 8 3 ) + ( x + 0 7 + x + 1 − 5 )
x + 2 1 + x 7 − x + 1 5 + x + 8 3 = 0 x ( x + 2 ) 8 x + 1 4 − ( x + 1 ) ( x + 8 ) 2 x + 3 7 = 0 On further simplication of last equation we get 6 x 3 + 4 5 x 2 + 1 1 6 x + 1 1 2 = 0 ( 2 x + 7 ) ( 3 x 2 + 1 2 x + 1 6 ) = 0 2 x + 7 = 0 3 x 2 + 1 2 x + 1 6 = 0 One of the value we have x = − 2 7 , the discriminant of quadratic equation is D < 0 , which gives no real solution in x .
Only real solution of x is − 2 7 . Therefore, ∣ x ∣ = 3 . 5