Advertisements
Advertisements
प्रश्न
The sum of two number a and b is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers a and b.
Advertisements
उत्तर
Given that a and b be two numbers in such a way that b = (15 - a).
Then according to question
`1/a+1/b=3/10`
`(b + a)/(ab)=3/10`
`(a + b)/(ab)=3/10`
By cross multiplication
10a + 10b = 3ab ........ (1)
Now putting the value of b in equation (1)
10a + 10(15 - a) = 3a(15 - a)
10a + 150 - 10a = 45a - 3a2
150 = 45a - 3a2
3a2 - 45a + 150 = 0
3(a2 - 15a + 50) = 0
(a2 - 15a + 50) = 0
a2 - 10a - 5a + 50 = 0
a(a - 10) - 5(a - 10) = 0
(a - 10)(a - 5) = 0
a - 10 = 0
a = 10
Or
a - 5 = 0
a = 5
Therefore,
When a = 10 then
b = 15 - a = 15 - 10 = 5
And when a = 5 then
b = 15 - a = 15 - 5 = 10
Thus, two consecutive number be either a = 5, b = 10 or a = 10, b = 5.
APPEARS IN
संबंधित प्रश्न
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
Solve the following quadratic equations by factorization:
x2 - x - a(a + 1) = 0
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
Solve for x: `3x^2-2sqrt3x+2=0`
Solve the following quadratic equations by factorization:
\[\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}; x \neq 3, 5\]
If the equation x2 − ax + 1 = 0 has two distinct roots, then
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
Solve equation using factorisation method:
2x2 – 9x + 10 = 0, when:
- x ∈ N
- x ∈ Q
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.
A two digit number is such that the product of its digit is 14. When 45 is added to the number, then the digit interchange their places. Find the number.
Solve for x:
`(x + 1/x)^2 - (3)/(2)(x - 1/x)-4` = 0.
In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`
The length of a rectangle exceeds its breadth by 5 m. If the breadth were doubled and the length reduced by 9 m, the area of the rectangle would have increased by 140 m². Find its dimensions.
If the perimeter of a rectangular plot is 68 m and the length of its diagonal is 26 m, find its area.
Solve the following equation by factorisation :
x2 + 6x – 16 = 0
The product of two successive integral multiples of 5 is 300. Then the numbers are:
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
