Advertisements
Advertisements
Question
Five times a certain whole number is equal to three less than twice the square of the number. Find the number.
Advertisements
Solution
Let number = x
Now according to the condition,
5x = 2x2 - 3
⇒ 2x2 - 5x - 3 = 0
⇒ 2x2 - 6x + x - 3 = 0
⇒ 2x(x - 3) + 1 (x - 3) = 0
⇒ (x - 3)(2x + 1) = 0
Either x - 3 = 0,
then x = 3
or
2x + 1 = 0,
then 2x = -1
⇒ x `-(1)/(2)`
But it is not possible as the number is whole number.
∴ Number = 3.
APPEARS IN
RELATED QUESTIONS
Determine two consecutive multiples of 3, whose product is 270.
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
Solve each of the following equations by factorization:
`X^2 – 10x – 24 = 0 `
Solve the following equation : 5x2 - 11x + 2 = 0
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
Solve the following equation: `x^2 + (a + 1/a)x + 1 = 0`
A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.
An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.
The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.
