Advertisements
Advertisements
प्रश्न
The sum of two natural number is 28 and their product is 192. Find the numbers.
Advertisements
उत्तर
Let the required number be x and (28-x).
According to the given condition,
`x(28)-x=192`
⇒`28x-x^2=192`
⇒`x^2-28x+192=0`
⇒`x^2-16x-12x+192=0`
⇒`x(x-16)-12(x-16)=0`
⇒`(x-12)(x-16)=0`
⇒`x-12=0 or x-16=0`
⇒`x=12 or x=16`
when` x=12`
`28-x=28-12=16`
when `x=16`
28-x=28-16=12`
Hence, the required numbers are 12 and 16.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
9x2 − 3x − 2 = 0
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.
A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
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.
Solve of the following equations, giving answer up to two decimal places.
3x2 – x – 7 =0
Solve each of the following equations by factorization:
`9/2x=5+x^2`
Solve the given quadratic equation for x : 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0 ?
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\] has equal roots, find the value of k.
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
Show that x = −3 is a solution of x2 + 6x + 9 = 0.
Solve the following equation: a2b2x2 + b2x - a2x - 1 = 0
A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
Solve the following by reducing them to quadratic form:
`sqrt(x^2 - 16) - (x - 4) = sqrt(x^2 - 5x + 4)`.
In each of the following, determine whether the given values are solution of the given equation or not:
`a^2x^2 - 3abx + 2b^2 = 0; x = a/b, x = b/a`.
The sum of the numerator and denominator of a certain positive fraction is 8. If 2 is added to both the numerator and denominator, the fraction is increased by `(4)/(35)`. Find the fraction.
