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 for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
Solve of the following equations, giving answer up to two decimal places.
3x2 – x – 7 =0
Solve each of the following equations by factorization:
`x=(3x+1)/(4x)`
Solve the following quadratic equations by factorization:
(x + 1) (2x + 8) = (x+7) (x+3)
Solve for x: `3x^2-2sqrt3x+2=0`
Solve the following quadratic equations by factorization:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
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" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
Solve the following equation: `("a+b")^2 "x"^2 - 4 "abx" - ("a - b")^2 = 0`
Find two natural numbers which differ by 3 and whose squares have the sum of 117.
Find two consecutive positive even integers whose squares have the sum 340.
Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0
Solve the following quadratic equation by factorisation:
(2x + 3) (3x - 7) = 0
Paul is x years old and his father’s age is twice the square of Paul’s age. Ten years hence, the father’s age will be four times Paul’s age. Find their present ages.
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
Find the roots of the quadratic equation x2 – x – 2 = 0.
