Advertisements
Advertisements
Question
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
Advertisements
Solution
Let three consecutive integer be x, (x + 1) and (x + 2)
Then according to question
x2 + (x + 1)(x + 2) = 46
x2 + x2 + 3x + 2 = 46
2x2 + 3x + 2 - 46 = 0
2x2 + 3x - 44 = 0
2x2 - 8x + 11x - 44 = 0
2x(x - 4) + 11(x - 4) = 0
(x - 4)(2x + 11) = 0
x - 4 = 0
x = 4
Or
2x + 11 = 0
2x = -11
x = -11/2
Since, x being a positive number, so x cannot be negative.
Therefore,
When x = 4 then other positive integer
x + 1 = 4 + 1 = 5
And
x + 2 = 4 + 2 = 6
Thus, three consecutive positive integer be 4, 5, 6.
RELATED QUESTIONS
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:
`2/2^2-5/x+2=0`
Solve the following quadratic equations by factorization:
`x^2-(sqrt2+1)x+sqrt2=0`
Two squares have sides x cm and (x + 4) cm. The sum of this areas is 656 cm2. Find the sides of the squares.
The sum of a numbers and its positive square root is 6/25. Find the numbers.
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples.
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
If one of the equation x2 + ax + 3 = 0 is 1, then its other root is
Solve the following equation: 2x2 - x - 6 = 0
Solve the following equation: 25x (x + 1) = -4
Solve the Following Equation : x2- x - a (a + 1) = o
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.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3`sqrt(3)` + 6 = 0; x = `sqrt(3)`, x = -2`sqrt(3)`
Solve the following equation by factorization
4x2 = 3x
Solve the following equation by factorization
x2 – (p + q)x + pq = 0
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
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.
