Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the present age of Shikha be x years
Then, 8 years later, age of her = (x + 8) years
Five years ago, her age = (x - 5) years
Then according to question,
(x - 5)(x + 8) = 30
x2 + 8x - 5x - 40 = 30
x2 + 3x - 40 - 30 = 0
x2 + 3x - 70 = 0
x2 - 7x + 10x - 70 = 0
x(x - 7) + 10(x - 7) = 0
(x - 7)(x + 10) = 0
So, either
x- 7 = 0
x = 7
Or
x + 10 = 0
x = -10
But the age never be negative
Hence, the present age of Shikha be 7 years.
APPEARS IN
संबंधित प्रश्न
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
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?
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
The sum of a natural number and its square is 156. Find the number.
Solve the following quadratic equation by factorisation.
2y2 + 27y + 13 = 0
Solve the following quadratic equations by factorization: \[\frac{16}{x} - 1 = \frac{15}{x + 1}; x \neq 0, - 1\]
Solve the following quadratic equations by factorization:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
If the equation x2 − ax + 1 = 0 has two distinct roots, then
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 =
The values of k for which the quadratic equation \[16 x^2 + 4kx + 9 = 0\] has real and equal roots are
Solve the following equation: (x-8)(x+6) = 0
Solve the following equation:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
Find two consecutive natural numbers whose squares have the sum 221.
Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
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.
