Question
Find two consecutive positive even integers whose product is $288.$
✓
Answer
Let the required consecutive positive even integers be x and $(x + 2).$
Then, we have
$ x \times(x+2)=288$
$ \Rightarrow x^2+2 x-288=0$
$ \Rightarrow x^2+18 x-16 x-288=0$
$ \Rightarrow x(x+18)-16(x+18)=0$
$ \Rightarrow(x+18)(x-16)=0$
$ \Rightarrow x+18=0 \text { or } x-16=0$
$ \Rightarrow x=-18 \text { or } x=16$
$\text { Since } x \text { is a positive integer, } x \neq-18$
$ \Rightarrow x=16$
$ \Rightarrow x+2=16+2=18$
Hence, the required consecutive positive even integers are $16$ and $18.$
Then, we have
$ x \times(x+2)=288$
$ \Rightarrow x^2+2 x-288=0$
$ \Rightarrow x^2+18 x-16 x-288=0$
$ \Rightarrow x(x+18)-16(x+18)=0$
$ \Rightarrow(x+18)(x-16)=0$
$ \Rightarrow x+18=0 \text { or } x-16=0$
$ \Rightarrow x=-18 \text { or } x=16$
$\text { Since } x \text { is a positive integer, } x \neq-18$
$ \Rightarrow x=16$
$ \Rightarrow x+2=16+2=18$
Hence, the required consecutive positive even integers are $16$ and $18.$
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
Solve the following quadratic equations by factorization:
$\frac{16}{\text{x}}-1=\frac{15}{\text{x}+1},$ $\text{x}\neq0,-1$
→$\frac{16}{\text{x}}-1=\frac{15}{\text{x}+1},$ $\text{x}\neq0,-1$
One card is drawn from a well$-$shuffled deck of $52$ cards. Find the probability of drawing:
→- An ace.
- A $'4'$ cf spades.
- A $'9'$ of a black suit.
- A red king.
In a class test, the sum of Kamal's marks in Mathematics and English is $40$. Had he got $3$ marks more in Mathematics and $4$ marks less in English, the product of the marks would have been $360$. Find his marks in two subjects separately.
→Ritu can row downstream $20\ km$ in $2$ hours, and upstream $4\ km$ in $2$ hours. Find her speed of rowing in still water and the speed of the current.
→In the given figure, if $AB || CD$, find the value of $x.$
→The following table shows the marks scored by $140$ students in an examination of a certain paper:
Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.
→| Marks | $0-12$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
| Number of students | $20$ | $24$ | $40$ | $36$ | $20$ |
If the zeros of the polynomial $f(x) = ax^3+ 3bx^2+ 3cx + d$ are in A.P., prove that $2b^3- 3abc + a^2d = 0.$
→Show that points $A(-5,6), B(3,0)$ and $C(9,8)$ are the vertices of an isosceles right-angled triangle. Calculate its area.
→Solve for x and y:
$217x + 131y = 913,$
$131x + 217y = 827$
→$217x + 131y = 913,$
$131x + 217y = 827$
The following distribution gives the state-wise teachers-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures:
→| Number of students per teacher | Number of states/U.T. |
| $15 - 20$ | $3$ |
| $20 - 25$ | $8$ |
| $25 - 30$ | $9$ |
| $30 - 35$ | $10$ |
| $35 - 40$ | $3$ |
| $40 - 45$ | $0$ |
| $45 - 50$ | $0$ |
| $50 - 55$ | $2$ |