Advertisements
Advertisements
Question
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?
Advertisements
Solution
Let three consecutive integer be x , (x + 1) and (x + 2)
Then according to question
x2 + (x + 1)(x + 2) = 154
x2 + x2 + 3x + 2 = 154
2x2 - 3x + 2 - 154 = 0
2x2 + 3x - 152 = 0
2x2 - 16x - 19x - 152 = 0
2x(x - 8) + 19(x - 8) = 0
(x - 8)(2x + 19) = 0
(x - 8) = 0
x = 8
Or
2x + 19 = 0
2x = -19
x = -19/2
Since, x being a positive number, so x cannot be negative.
Therefore,
Whenx = 8then other positive integer
x + 1 = 8 + 1 = 9
And
x + 2 = 8 + 2 = 10
Thus, three consecutive positive integer be 8, 9, 10.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation by factorization method : `x^2-5x+6=0`
Find the roots of the following quadratic equation by factorisation:
x2 – 3x – 10 = 0
Find the roots of the following quadratic equation by factorisation:
100x2 – 20x + 1 = 0
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 equation by factorization method : `3x^2-29x+40=0`
Solve the following quadratic equations by factorization:
5x2 - 3x - 2 = 0
Solve the following quadratic equations by factorization:
`(x-1/2)^2=4`
Solve the following quadratic equations by factorization:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
Solve the following quadratic equations by factorization:
`7x + 3/x=35 3/5`
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
Solve:
(a + b)2x2 – (a + b)x – 6 = 0; a + b ≠ 0
Solve each of the following equations by factorization:
`2x^2-1/2x=0`
Solve each of the following equations by factorization:
`9/2x=5+x^2`
Find the values of p for which the quadratic equation
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
