Question

8. Five times a certain whole number is equal to three
less than twice the square of the number. Find the
number.
(CSE)​

Answer 1

Answer:

$</p><p> \huge \star{{ \large \bold \pink{question}}}$

Five times a certain whole number is equal to three less than twice the square of the number. Find thenumber.

$\huge \star\huge \bold \red{solution}$

$let \: the \: number \: \: be \: x$

so ,according to the question

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

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

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

Let us factorize,

2x²−6x+x−3=0

2x(x−3)+1(x−3)=0

(x−3)(2x+1)=0

So

(x−3)=0 or (2x+1)=0

x=3 or 2x= −1

x=3 or x=−1/2

∴ The required number is

$\huge \bold \purple{3}$

[ since, −1/2 cannot be a whole number ]

Answer 2

Answer:

so ,according to the question

5x = {2x}^{2} - 35x=2x

2

−3

{2x}^{2} = 3 - 5x - 02x

2

=3−5x−0

{2x}^{2} - 5x - 3 = 02x

2

−5x−3=0

Let us factorize,

2x²−6x+x−3=0

2x(x−3)+1(x−3)=0

(x−3)(2x+1)=0

So

(x−3)=0 or (2x+1)=0

x=3 or 2x= −1

x=3 or x=−1/2

∴ The required number is

$\huge \bold \purple{3}$

[ since, −1/2 cannot be a whole number ]