Advertisements
Advertisements
рдкреНрд░рд╢реНрди
Determine two consecutive multiples of 3, whose product is 270.
Advertisements
рдЙрддреНрддрд░
Let the two consecutive multiples of 3 are 3x and 3x + 3
Given that their product is 270
⇒ (3x) (3x + 3) = 270
⇒ x(3x + 3) = 90
⇒ ЁЭСе2 + ЁЭСе - 30 = 0
⇒ ЁЭСе2 + 6ЁЭСе - 5ЁЭСе - 30 = 0
⇒ x(x + 6) - 5(x + 6) = 0
⇒ (x + 6) (x - 5) = 0
⇒ x = 5 or x = -6
Considering the positive value of x.
⇒ x = 5, 3x = 15 and 3x + 3 = 18
∴ The two consecutive multiples of 3 are 15 and 18.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Solve the following quadratic equation by factorization method : `x^2-5x+6=0`
Solve for x
`(2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3,`
Find two consecutive positive integers, sum of whose squares is 365.
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 two numbers is 48 and their product is 432. Find the numbers?
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
`4x^2+4sqrt3x+3=0`
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
the return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.
Solve the following equation by factorization
21x2 – 8x – 4 = 0
Solve the following equation by factorization:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
Solve the following equation by factorization
`x/(x + 1) + (x + 1)/x = (34)/(15)`
In an auditorium, the number of rows are equal to the number of seats in each row.If the number of rows is doubled and number of seats in each row is reduced by 5, then the total number of seats is increased by 375. How many rows were there?
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
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.
Find the roots of the quadratic equation x2 – x – 2 = 0.
