Question

if the sum of the square of the number and 4 time the number is 21,what is the number
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Answer 1

Let the number be 'X',

then,

A.T.Q

=> X^2 + 4X = 21

=> X^2 + 4X - 21 = 0

( by middle splitting term Factorisation)

=> X^2 + [7+(-3)] X - 21 = 0

( where a=1, b=4=[7+(-3)], c=-21=[7×(-3)] )

=> X^2 + 7X - 3X - 21 = 0

=> X( X + 7) -3( X + 7) = 0

=> (X-3)×(X+7) = 0

i) (X-3) = 0

=> X = 3

ii) (X+7) = 0

=> X = -7

So, Here can be two values of 'X', which are 3 & -7.