Question

4. ( a ) Simplify 3x (4x - 5) + 3 and find its
values for
(i)x = 3 (ii) x =½​

Answer 1

Answer:

Given,

3x(4x - 5) + 3

To Find :-

Simplify it and find values for :-

1) x = 3

2) x = $\sf\dfrac{1}{2}$

Solution :-

3x(4x - 5) + 3

$\sf 3x\times (4x - 5) + 3$

$\sf 3x\times(4x) - 3x\times(5) + 3$

$\sf 12x^{2} - 15x + 3$

Now,

1) x = 3

Substituting in :- $\sf 12x^{2} - 15x + 3$

$\sf 12(3)^{2} - 15(3) + 3$

= 12(9) - 45 + 3

= 108 - 45 + 3

= 111 - 45

= 66.

$\sf\therefore Value \:of \:x \:in \:12x^{2} - 15x + 3 = 66$

2) x = $\sf\dfrac{1}{2}$

Substituting value of x in :- $\sf 12x^{2} - 15x + 3$

$\sf 12(\dfrac{1}{2})^{2} - 15(\dfrac{1}{2}) + 3$

$\sf 12(\dfrac{1}{4})- \dfrac{15}{2} + 3$

3- $\sf\dfrac{15}{2} + 3$

Taking L.C.M as 2 :-

$(3 \times \frac{2}{2}) - \frac{15}{2 } + (3 \times \frac{2}{2} )$

$\frac{6}{2} - \frac{15}{2} + \frac{6}{2}$

$\frac{6 - 15 + 6}{2}$

$\frac{12 - 15}{2}$

$\frac{ - 3}{2}$

$\sf\therefore Value\: of \:x\: in\: 12x^{2} - 15x + 3 =\dfrac{-3}{2}$

Answer 2

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-- :

3x(4x−5)+3=12x^2−15x+3

x=3 gives the value 12(9)−15×3+3

                             =108−45+3

                              =66

x=1/2 gives the value 12(1/4)−15×(1/2)+3

                             =3−7.5+3

                              = - 3/2