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 by factorization:
6x2 + 11x + 3 = 0
Solve the following quadratic equations by factorization:
3x2 − 14x − 5 = 0
The product of two successive integral multiples of 5 is 300. Determine the multiples.
Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.
A two digit number is four times the sum and 3 times the product of its digits, find the number.
One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.
In an auditorium, the number of rows are equal to the number of seats in each row.If the number of rows is doubled and number of seats in each row is reduced by 5, then the total number of seats is increased by 375. How many rows were there?
Solve the quadratic equation by factorisation method:
x2 – 15x + 54 = 0
