Advertisements
Advertisements
प्रश्न
The sum of natural number and its reciprocal is `65/8` Find the number
Advertisements
उत्तर
Let the natural number be x.
According to the given condition,
`x+1/x=65/8`
⇒`(x^2+1)/x=65/8`
⇒`8x^2+8=65x`
⇒`8x^2-65x+8=0`
⇒`8x^2-64x-x+8=0`
⇒`8x(x-8)-1(x-8)=0`
⇒`(x-8)(8x-1)=0`
⇒`x-8=0 or 8x-1=0`
⇒`x=8 or x=1/8`
∴x=8 (x is a natural number)
Hence, the required number is 8.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`4sqrt3x^2+5x-2sqrt3=0`
Solve the following quadratic equations by factorization:
`x^2-(sqrt2+1)x+sqrt2=0`
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
Solve the following quadratic equations by factorization:
a2b2x2 + b2x - a2x - 1 = 0
A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
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.
Solve : x2 – 11x – 12 =0; when x ∈ N
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Divide 57 into two parts whose product is 680.
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 the sum of the roots of the equation \[x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0\] is equal to half of their product, then k =
The values of k for which the quadratic equation \[16 x^2 + 4kx + 9 = 0\] has real and equal roots are
Solve equation using factorisation method:
`x + 1/x = 2.5`
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
Solve the following equation by factorization
`(x^2 - 5x)/(2)` = 0
Solve the following equation by factorization
(x – 3) (2x + 5) = 0
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
Find two consecutive integers such that the sum of their squares is 61
Solve the following equation by factorisation :
x(x + 1) + (x + 2)(x + 3) = 42
