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
`x^2-4x+1=0`
The sum of two natural number is 28 and their product is 192. Find the numbers.
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
