Advertisements
Advertisements
Question
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
Advertisements
Solution
Let three consecutive natural numbers be x, x + 1 and x + 2.
Then according to problem
(x)2 = (x + 1)2 + (x + 2)2 = 110
⇒ x2 + x2 + 1 + 2x + x2 + 4 + 4x - 110 = 0
⇒ 3x2 + 6x - 105 = 0
⇒ x2 + 2x - 35 = 0
⇒ x2 + 7x - 5x - 35 = 0
⇒ x(x + 7) - 5(x + 7) = 0
⇒ (x + 7) (x - 5) = 0
⇒ x + 7 = 0 or x - 5 = 0
⇒ x = -7 or x = 5
But x = -7 is rejected as it is not a natural number.
Then x = 5
Hence, required numbers are 5, (5 + 1), (5 + 2) i.e., 5, 6 and 7.
RELATED QUESTIONS
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
The sum of the squares of the two consecutive odd positive integers as 394. Find them.
`x^2+8x-2=0`
Solve the following quadratic equations by factorization: \[\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3}; x \neq 5, 7\]
Solve the following equation: `7"x" + 3/"x" = 35 3/5`
The area of a right-angled triangle is 600 cm2. If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.
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.
Solve the following equation by factorisation :
x2 + 6x – 16 = 0
The product of two successive integral multiples of 5 is 300. Then the numbers are:
