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
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
Solve the following quadratic equations by factorization:
`(3x-2)/(2x-3)=(3x-8)/(x+4)`
Solve the following quadratic equation by factorisation.
2y2 + 27y + 13 = 0
If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.
Find the value of p for which the quadratic equation
\[\left( p + 1 \right) x^2 - 6(p + 1)x + 3(p + 9) = 0, p \neq - 1\] has equal roots. Hence, find the roots of the equation.
Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
Solve the following equation by factorization
(x – 4)2 + 52 = 132
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
