The difference of a positive and its square is -30. Find the number?
Answers
Answer:
6
Step-by-step explanation:
Let us consider the positive number = x
A/c to problem
Difference of positive number & its square is - 30
=> x - x^2 = -30
=> x^2 - x - 30 = 0
Spliting the quadratic equation
=> x^2 - 6x + 5x - 30 =0
Taking x & 5 as common from the equation we have
=> x(x-6) + 5(x-6) = 0
Now taking x-6 as common we have
=> (x-6)(x+5) = 0
=> x-6 =0 & x+5 =0
=> x = 6 & x = -5
As we consider x is a positive number we have x as 6
i.e x = 6.
Verification
=> 6 - 6^2
=> 6 - 36
=> - 30
Given : The difference of a positive and its square is -30.
To Find : the Number
Solution:
Let say number is N
Square = N²
Difference is N - N²
Difference is - 30
N - N² = - 30
=> N² - N - 30 = 0
=> N² - 6N + 5N - 30 = 0
=> N (N - 6) + 5(N - 6) = 0
=> ( N + 5)(N - 6) = 0
=> N = 6 or - 5
as Number if Positive hence -5 is neglected
so N = 6
Number is 6
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