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
Solve the following quadratic equations by factorization:
(x − 4) (x + 2) = 0
Solve the following quadratic equations by factorization:
6x2 + 11x + 3 = 0
A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
Solve : x2 – 11x – 12 =0; when x ∈ N
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Solve the following quadratic equations by factorization: \[\frac{x - 4}{x - 5} + \frac{x - 6}{x - 7} = \frac{10}{3}; x \neq 5, 7\]
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the roots are both equal to
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
If 2 is a root of the equation x2 + ax + 12 = 0 and the quadratic equation x2 + ax + q = 0 has equal roots, then q =
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
A two digit number is four times the sum and 3 times the product of its digits, find the number.
If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.
Solve for x:
`(x + 1/x)^2 - (3)/(2)(x - 1/x)-4` = 0.
Solve the following equation by factorization
x (2x + 1) = 6
Solve the following equation by factorization
x(6x – 1) = 35
Solve the following equation by factorization
(x – 4)2 + 52 = 132
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
