Advertisements
Advertisements
प्रश्न
The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers .
Advertisements
उत्तर
Let the required natural numbers be x and(9'-x).
According to the given condition,
`1/x+1/(9-x)=1/2`
⇒`(9-x+x)/(x(9-x))=/12`
⇒`9/(9x-x^2)=1/2`
⇒`9x-x^2=18`
⇒`x^2-9x+18=0`
⇒`x^2-6x-3x+18=0`
⇒`x(x-6)-3(x-6)=0`
⇒`x-3=0 or x-6=0`
⇒`x=3 or x=6`
When `x=3`
`9-x=9-3=6`
When` x=6`
`9-x=9-6=3`
Hence, the required natural numbers are 3 and 6.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
(x − 4) (x + 2) = 0
Solve the following quadratic equations by factorization:
4x2 + 5x = 0
Solve the following quadratic equations by factorization:
48x2 − 13x − 1 = 0
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
The sum of two natural numbers is 20 while their difference is 4. Find the numbers.
If the equation x2 + 4x + k = 0 has real and distinct roots, then
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:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
Solve the following quadratic equation by factorisation:
9x2 - 3x - 2 = 0
Solve the equation:
`6(x^2 + (1)/x^2) -25 (x - 1/x) + 12 = 0`.
In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈Q
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
Find the roots of the quadratic equation x2 – x – 2 = 0.
