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
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
The sum of a numbers and its positive square root is 6/25. Find the numbers.
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Solve of the following equations, giving answer up to two decimal places.
3x2 – x – 7 =0
The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
Solve the following quadratic equations by factorization:
\[9 x^2 - 6 b^2 x - \left( a^4 - b^4 \right) = 0\]
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
Solve the following equation: `10"x" - 1/"x" = 3`
Solve the following equation: `"x"^2 - ( sqrt 2 + 1) "x" + sqrt 2 = 0 `
Solve the following equation : `"x"^2 - 4 sqrt 2 "x" + 6 = 0 `
Solve the following equation: `x^2 + (a + 1/a)x + 1 = 0`
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.
Solve: x(x + 1) (x + 3) (x + 4) = 180.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
Solve the following equation by factorization
`(x^2 - 5x)/(2)` = 0
A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.
Find the roots of the following quadratic equation by the factorisation method:
`2x^2 + 5/3x - 2 = 0`
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
