Advertisements
Advertisements
प्रश्न
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
Advertisements
उत्तर
Let the smaller numbers be x
Then according to question,
The larger number be = 2x - 5, then
(2x - 5)2 - x2 = 88
4x2 - 20x + 25 - x2 - 88 = 0
3x2 - 20x - 63 = 0
3x2 - 27x + 7x - 63 = 0
3x(x - 9) + 7(x - 9) = 0
(x - 9)(3x + 7) = 0
x - 9 = 0
x = 9
Or
3x + 7 = 0
3x = -7
x = -7/3
Since, x being a positive integer so, x cannot be negative,
Therefore,
When x = 9 then larger number be
2x - 5 = 2(9) - 5 = 18 - 5 = 13
Thus, two consecutive number be either 9, 13.
APPEARS IN
संबंधित प्रश्न
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solve the following quadratic equations by factorization:
4x2 + 5x = 0
Solve the following quadratic equations by factorization:
(a + b)2x2 - 4abx - (a - b)2 = 0
Solve the following quadratic equations by factorization:
abx2 + (b2 – ac)x – bc = 0
There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?
A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number
The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.
Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
Solve each of the following equations by factorization:
x(x – 5) = 24
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
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 `sqrt (2/3)` is a solution of equation 3x2 + mx + 2 = 0, find the value of m.
Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.
Find two consecutive integers such that the sum of their squares is 61
The hypotenuse of grassy land in the shape of a right triangle is 1 metre more than twice the shortest side. If the third side is 7 metres more than the shortest side, find the sides of the grassy land.
At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than `t^2/4` minutes. Find t.
If the area of a square is 400 m2, then find the side of the square by the method of factorization.
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.
(x – 3) (x + 5) = 0 gives x equal to ______.
If `x + 1/x = 2.5`, the value of x is ______.
