Two number differ by 4 and their product is 192. Find the numbers… - Vidyadip

Question

Two number differ by $4$ and their product is $192$. Find the numbers.

✓

Answer

Let first number $= x$
Then second number $= x - 4$
According to the condition,
$ \Rightarrow x(x-4)=192 $
$ \Rightarrow x^2-4 x-192=0 $
$ \Rightarrow x^2-16 x+12 x-192=0 $
$ \Rightarrow x(x-16)+12(x-16)=0 $
$ \Rightarrow(x-16)(x+12)=0$
Either $x - 16 = 0,$ then $x = 16$
Or $x + 12 = 0,$ then $x = -12$

If $x = 16$, then

First number $= 16$ and second number $= 16 - 4 = 12$

If $x = -12,$ then

First number = -12 and second number $= -12 - 4 = -16$
Hence numbers are $16, 12$ or $-12, -16$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

A passenger train takes $2$ hours less for a journey of $300\ km$ if its speed is increased by $5\ km/hr$ from its usual speed. Find the usual speed of the train.

Find the area of a parallelogram $ABCD$ if three of its vertices are $A(2, 4)$, $\text{B}(2+\sqrt{3},\ 5)$ and $C(2, 6).$

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:
$\text{f(x)}=\text{x}^2-\big(\sqrt{3}+1\big)\text{x}+\sqrt{3}$

Solve the following systems of equations:
$\frac{\text{xy}}{\text{x}+\text{y}}=\frac{6}{5}$
$\frac{\text{xy}}{\text{y}-\text{x}}=6$ where $\text{x}+\text{y}\neq0,\text{y}-\text{x}\neq0.$

Solve the following system of equations by the method of cross-multiplication:

$ a^2 x+b^2 y=c^2$
$ b^2 x+a^2 y=d^2$

The volume of a hemi-sphere is $2425cm^3$. Find its curved surface area. $\Big(\text{use}\ \pi=\frac{22}{7}\Big)$

Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:
$x - y + 3 = 0, 2x + 3y - 4 = 0$

From a cubical piece of wood of side $21\ cm$, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece. Find the surface area and volume of the remaining piece.

Solve the following quadratic equations by factorization:
$\frac{1}{\text{x}-2}+\frac{2}{\text{x}-1}=\frac{6}{\text{x}},$ $\text{x}\neq0$

The angle of elevation of the top of building from the foot of a tower is $30^{\circ}$. The angle of elevation of the top of the tower from the foot of the building is $60^{\circ}$. If the tower is $60^{\circ}$. If the tower is $60 \ m$ high, Find the height of the building.