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,
$\Rightarrow x(x - 4) = 192$
$\Rightarrow x^2 - 4x - 192 = 0$
$\Rightarrow x^2 - 16x + 12x - 192 = 0$
$\Rightarrow x(x - 16) + 12(x - 16) = 0$
$\Rightarrow (x - 16)(x + 12) = 0$
Either x - 16 = 0, then x = 16
Or x + 12 = 0, then x = -12
Hence numbers are 16, 12 or -12, -16
Then second number = x - 4
According to the condition,
$\Rightarrow x(x - 4) = 192$
$\Rightarrow x^2 - 4x - 192 = 0$
$\Rightarrow x^2 - 16x + 12x - 192 = 0$
$\Rightarrow x(x - 16) + 12(x - 16) = 0$
$\Rightarrow (x - 16)(x + 12) = 0$
Either x - 16 = 0, then x = 16
Or x + 12 = 0, then x = -12
- If x = 16, then
- If x = -12, then
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.
Explore more
Similar questions
Name the quadrilateral formed, if any, by the following points, and given reason for your answers:
A(-3, 5), B(3, 1), C(0, 3), D(-1, -4).
A(-3, 5), B(3, 1), C(0, 3), D(-1, -4).
The product of Tanay's age $($in years$)$ five years ago and his age ten years later is $16.$ Determine Tanay's present age.
→A fraction becomes $\frac{9}{11}$ if is added to both numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes $\frac{5}{6}.$ Find the fraction.
→Form the pair of linear equations in the following problems, and find their solution graphically:
10 students of class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
10 students of class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
Four equal circles, each of radius 5cm, touch each other, as shown in the figure. Find the area included between them. $[\text{Take }\pi\ =3.14]$
→A cylindrical vessel with internal diameter 10cm and height 10.5cm is full of water. A solid cone of base diameter 7cm and height 6cm is completely immersed in water. Find the volume of water
- Displaced out of the cylinder
- Left in the cylinder.
Solve the following systems of equations by using the method of cross multiplication:
$\frac{\text{a}}{\text{x}}-\frac{\text{b}}{\text{y}}=0$
$\frac{\text{ab}^2}{\text{x}}+\frac{\text{a}^2\text{b}}{\text{y}}=\text{a}^2+\text{b}^2,$ where $\text{x}\neq0$ and $\text{y}\neq0$
→$\frac{\text{a}}{\text{x}}-\frac{\text{b}}{\text{y}}=0$
$\frac{\text{ab}^2}{\text{x}}+\frac{\text{a}^2\text{b}}{\text{y}}=\text{a}^2+\text{b}^2,$ where $\text{x}\neq0$ and $\text{y}\neq0$
Find all possible values of y for which the distance between the points A(2, -3) and B(10, y) is 10 units.
How many three-digit natural numbers are divisible by 7?
The sum of four consecutive numbers in $A.P$. is $32$ and the ratio of the product of the first and last terms to the product of two middle terms is $7 : 15.$ Find the number.
→