Advertisements
Advertisements
प्रश्न
Find two consecutive multiples of 3 whose product is 648.
Advertisements
उत्तर
Le the required consecutive multiples of 3 be 3x and`3(x+1)`
According to the given condition,
`3x xx3(x+1)=648`
⇒`9(x^2+x)=648`
⇒` x^2+x=72`
⇒`x^2+x-72=0`
⇒`x^2+x-72=0`
⇒`x^2+9x-8x-72=0`
⇒`x(x+9)-8(x+9)=0`
⇒`(x+9)(x-8)=0`
⇒`x+9=0 or x-8=0`
⇒` x=-9 or x=8`
∴` x=8` (Neglecting the negative value)
When `x=8`
`3x=3xx8=24`
`3(x+1)=3xx(8+1) =3xx9=27`
Hence, the required multiples are 24 and 27.
APPEARS IN
संबंधित प्रश्न
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
Solve the following quadratic equations by factorization:
`x^2-4sqrt2x+6=0`
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
Solve the following quadratic equation by factorization:
`sqrt(6)x^2 - 4x - 2sqrt(6) = 0`
Solve each of the following equations by factorization:
`2x^2-1/2x=0`
Solve each of the following equations by factorization :
`6/x=1+x`
Solve each of the following equations by factorization:
`x=(3x+1)/(4x)`
Solve the following quadratic equations by factorization:
`4(2x – 3)^2 – (2x – 3) – 14 = 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.
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
If 2 is a root of the equation x2 + ax + 12 = 0 and the quadratic equation x2 + ax + q = 0 has equal roots, then q =
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
Solve equation using factorisation method:
(2x – 3)2 = 49
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
Solve the following quadratic equation by factorisation method:
`x/(x + 1) + (x + 1)/x = (34)/(15') x ≠ 0, x ≠ -1`
The hypotenuse of a right-angled triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
