Question

A two digit number is made of two consecutive digits such that the sum of the square is 4 less than the number find the two digit number

Answer 1

GIVEN :-

A two digit number is made of two consecutive digits such that the sum of the square is 4 less than the number.

TO FIND :- The two digit number

SOLUTION :-

Let one digit be x at tens place

Other will be x + 1 at once place

The number can be written as

10x + (x+1)

ACCORDING TO THE QUESTION ;

x^2 + (x+1)^2 + 4 = 10x + (x+1)

Now, we shall solve this quadratic Equation :-

${x}^{2} + {(x + 1)}^{2} + 4 = 10x + x + 1 \\ \\ \\ \implies {x}^{2} + {x}^{2} + 1 + 2x + 4 = 11x + 1 \\ \\ \\ \implies 2 {x}^{2} + 5 + 2x = 11x + 1 \\ \\ \\ \implies 2 {x}^{2} - 9x + 4 = 0 \\ \\ \\ \implies 2 {x}^{2} - 8x - x + 4 = 0 \\ \\ \\ \implies 2x(x - 4) - 1(x - 4) = 0\\ \\ \\ \implies (x - 4)(2x - 1) = 0 \\ \\ \\ \implies \boxed{x = 4 \: or \: x = \frac{1}{2} }$

But x cannot be 1/2 so x =4

Therefore the number is 45.

Answer 2

Step-by-step explanation:

the correct answer is 45