Advertisements
Advertisements
рдкреНрд░рд╢реНрди
Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.
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
Find two consecutive positive integers, sum of whose squares is 365.
The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.
The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
`x^2-4x+1=0`
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more then each would have got Rs. 12 less. Find ‘x’.
Solve the following equation by factorization
`(2)/(3)x^2 - (1)/(3)x` = 1
Solve the following equation by factorization
`sqrt(3x + 4) = x`
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
Find the roots of the following quadratic equation by the factorisation method:
`3x^2 + 5sqrt(5)x - 10 = 0`
