(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

Solve the following equation by factorization

`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`

Solve the following equation by factorization

`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`

Solve the following equation by factorization

`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`

Solve the following equation by factorization

`sqrt(3x + 4) = x`

Solve the following equation by factorization

`sqrt(x(x - 7)) = 3sqrt(2)`

Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )² + 6(3x + 1) – 8 = 0

Find the values of x if p + 1 =0 and x² + px – 6 = 0

Find the values of x if p + 7 = 0, q – 12 = 0 and x² + px + q = 0,

If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.

Find two consecutive natural numbers such that the sum of their squares is 61.

Find two consecutive integers such that the sum of their squares is 61

If the product of two positive consecutive even integers is 288, find the integers.

If the product of two consecutive even integers is 224, find the integers.

Find two consecutive even natural numbers such that the sum of their squares is 340.

Find two consecutive odd integers such that the sum of their squares is 394.

The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.

Five times a certain whole number is equal to three less than twice the square of the number. Find the number.

Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.

The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.

There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?