Question

five times a positive whole number is 3 less than twice the square of the number and the number is​

Answer 1

GIVEN :-

Five times a positive whole number is 3 less than twice the square of the number.

Let the unknown number be x

According to the Question,

$5x + 3 = 2 {x}^{2}$

Now, we shall solve this quadratic equation by formula method.

$2 {x}^{2} - 5x - 3 = 0$

a=2

b= -5

c = -3

Discriminant (D) = b^2 - 4ac

25 + 4 × 2× 3

= 25 + 24

= 49

FORMULA :-

$x = \frac{ - b \pm \sqrt{d} }{2a}$

$x = \frac{ 5 + 7}{4} \: \: or \: \frac{5 - 7}{4} \\ \\ \\ = 3 \: \: \: or \: \: \frac{ - 1}{2}$

But in question it is given positive integer. So the answer is 3.

VERIFICATION :-

LHS = 5x + 3

= 5 × 3 + 3

= 15+ 3

= 18

RHS = 2x ^2

= 2 × 3 × 3

= 18

Hence, LHS = RHS OUR ANSWER IS CORRECT