Advertisements
Advertisements
Question
Find two consecutive natural numbers such that the sum of their squares is 61.
Advertisements
Solution
Let the first natural number = x
then second natural number = x + 1
According to the condition, (x)2 + (x + 1)2 = 61
⇒ x2 + x2 + 2x + 1 - 61 = 0
⇒ 2x2 + 2x - 60 = 0
⇒ x2 + x - 30 = 0
⇒ x2 + 6x - 5x - 30 = 0
⇒ x(x + 6) -5(x + 6) = 0
⇒ (x + 6)(x - 5) = 0
EIther x + 6 = 0,
then x = -6
or
x - 5 = 0,
then x = 5
∴ The number are positive.
∴ x = -6 is not possible
Hence the first natural number = 5
and secod natural number = 5 + 1 = 6.
APPEARS IN
RELATED QUESTIONS
Divide 29 into two parts so that the sum of the squares of the parts is 425.
Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
One of the roots of equation 5m2 + 2m + k = 0 is `(-7)/5` Complete the following activity to find the value of 'k'.
Write the set of values of k for which the quadratic equation has 2x2 + kx – 8 = 0 has real roots.
Solve the following equation : `"x"^2 - 4 sqrt 2 "x" + 6 = 0 `
The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.
Solve equation using factorisation method:
`2x^2 - 1/2x = 0`
The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
The roots of the equation x2 + 3x – 10 = 0 are ______.
