Advertisements
Advertisements
рдкреНрд░рд╢реНрди
Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.
Advertisements
рдЙрддреНрддрд░
Given that the sum of two numbers is 16.
Let the two numbers be x and 16 - x
By the given hypothesis, we have
`rArr1/x+1/(16-x)=1/3`
`rArr(16-x+x)/(x(16-x))=1/3`
⇒ 48 = 16x - x2
⇒ ЁЭСе2 - 16ЁЭСе + 48 = 0
⇒ ЁЭСе2 - 12ЁЭСе - 4ЁЭСе + 48 = 0
⇒ x(x - 12) - 4(x - 12) = 0
⇒ (x - 12) (x - 4) = 0
⇒ x = 12 or x = 4
∴ The two numbers are 4 and 12.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Solve the following quadratic equations by factorization:
9x2 − 3x − 2 = 0
Solve the following quadratic equations by factorization:
`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3
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 speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Ashu is x years old while his mother Mrs Veena is x2 years old. Five years hence Mrs Veena will be three times old as Ashu. Find their present ages.
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
`7x^2+3x-4=0`
The sum of the squares of two consecutive positive integers is 365. Find the integers.
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Solve the given quadratic equation for x : 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0 ?
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
Solve the following equation: `"m"/"n" "x"^2 + "n"/"m" = 1- 2"x"`
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
Solve equation using factorisation method:
(2x – 3)2 = 49
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
In each of the following, determine whether the given values are solution of the given equation or not:
`x^2 - sqrt(2) - 4 = 0; x = -sqrt(2), x = -2sqrt(2)`
The sum of the numerator and denominator of a certain positive fraction is 8. If 2 is added to both the numerator and denominator, the fraction is increased by `(4)/(35)`. Find the fraction.
