Advertisements
Advertisements
प्रश्न
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
Advertisements
उत्तर
Let Zeba’s age = x
According to the question,
(x – 5)2 = 11 + 5x
x2 + 25 – 10x = 11 + 5x
x2 – 15x + 14 = 0
x2 – 14x – x + 14 = 0
x(x – 14) – 1(x – 14) = 0
x = 1 or x = 14
We have to neglect 1 as 5 years younger than 1 cannot happen.
Therefore, Zeba’s present age = 14 years.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations
(i) 7x2 = 8 – 10x
(ii) 3(x2 – 4) = 5x
(iii) x(x + 1) + (x + 2) (x + 3) = 42
Solve the following quadratic equations by factorization:
`(x-1/2)^2=4`
Solve the following quadratic equations by factorization:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
Solve the following quadratic equations by factorization:
`2(x^2 – 6) = 3 ( x – 4)`
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:
- the age of the son five years ago.
- the present age of the woman.
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
2x2 – 9x + 10 = 0,when x∈N
Solve the following equation by factorization.
a2x2 + 2ax + 1 = 0, a ≠ 0
Solve the following equation by factorization:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
Solve the following equation by factorization
`sqrt(3x + 4) = x`
Find two consecutive natural numbers such that the sum of their squares is 61.
A wire ; 112 cm long is bent to form a right angled triangle. If the hypotenuse is 50 cm long, find the area of the triangle.
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
