Advertisements
Advertisements
Question
The sum of the squares of two consecutive positive integers is 365. Find the integers.
Advertisements
Solution
Let the required two consecutive positive integers be x and (x+1).
According to the given condition,
`x^2+(x+1)^2=365`
⇒`x^2+x^2+2x+1=365`
⇒`2x^2+2x-364=0`
⇒`x^2+x-182=0`
⇒`x^2+14x-13x-182=0`
⇒`x(x+14)-13(x+14)=0`
⇒`(x+14)(x-13)=0`
⇒`x+14=0 or x-13`
∴`x=13` (x is a positive integers)
When `x=13`
`x+1=13+1=14`
Hence, the required positive integers are 13 and 14.
RELATED QUESTIONS
Find two numbers whose sum is 27 and product is 182.
Solve the following quadratic equations by factorization:
`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1
Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.
Solve the following quadratic equation by factorisation.
2m (m − 24) = 50
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 quadratic equations by factorization: \[\frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x}; x \neq 0, - 1, 2\]
If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
If p and q are the roots of the equation x2 – px + q = 0, then ______.
If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
Solve the following equation: c
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
A two digit number is four times the sum and 3 times the product of its digits, find the number.
Solve equation using factorisation method:
`x + 1/x = 2.5`
Solve equation using factorisation method:
(2x – 3)2 = 49
The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.
Solve the following equation by factorization
`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`
If the product of two positive consecutive even integers is 288, find the integers.
If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm2. However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm2. Determine the sides of the two squares.
