Advertisements
Advertisements
प्रश्न
Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.
Advertisements
उत्तर
Ratio in two natural numbers = 3 : 4
Let the numbers be 3x and 4x
According to the condition,
(4x)2 - (3x)2 = 175
⇒ 16x2 - 9x2 = 175
⇒ 7x2 = 175
⇒ x2 = `(175)/(7)` = 25 = (±5)2
∴ x = 5, -5
But x - 5 is not a natural number
∴ x = 5
∴ Natural numbers are 3x, 4x
= 3 x 5, 4 x 5
= 15, 20.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations
(i) x2 + 5x = 0 (ii) x2 = 3x (iii) x2 = 4
The sum of a number and its reciprocal is 17/4. Find the number.
Solve:
`1/(x + 1) - 2/(x + 2) = 3/(x + 3) - 4/(x + 4)`
Solve the following quadratic equations by factorization: \[2 x^2 + ax - a^2 = 0\]
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
Solve the following quadratic equation by factorisation:
x2 + 3x - 18 = 0
Solve the following equation by factorization
`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
Solve the following equation by factorization
`(x + 1)/(x - 1) + (x - 2)/(x + 2)` = 3
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.
Find the roots of the following quadratic equation by the factorisation method:
`3x^2 + 5sqrt(5)x - 10 = 0`
