Question

find a number whose square diminished by 84 is equal to thrice 8 more than the given number

Answer 1

Answer:

Step-by-step explanation:

Let the unknown no. be x.

ATP:-

x^2 - 84 = 3(x+8)

x^2-84 =3x+24

x^2-3x-108=0

x^2-12x+9x-108=0

x(x-12)+ 9(x-12)=0

(x+9)(x-12)=0

Therefore, x=-9 and x=12

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Answer 2

Let number be x
According to question,
${x}^{2} - 84 =3(8 + x)$
$or \: {x}^{2} - 84 = 24 + 3x$
$or \: {x}^{2} - 3x - 108 = 0$
$or \: {x}^{2} - 12x + 9x - 108 = 0$
$x(x - 12) + 9(x - 12) = 0$
$or \: x - 12 = 0 \: and \: x + 9 = 0$
$therefore \: x = 12 \: or \: x = - 9$