Final answer:
To find the three consecutive even numbers whose squared sum is 1460, we represent them as x, x+2, and x+4. By forming and solving a quadratic equation, we get that the numbers are 20, 22, and 24. The correct answer is b. 20, 22, 24.
Step-by-step explanation:
The problem is to find three consecutive even natural numbers whose squares sum up to 1460. We can express these numbers as x, x+2, and x+4 where x is the smallest of the three even numbers. The equation can be set up as:
x^2 + (x+2)^2 + (x+4)^2 = 1460
Expanding and simplifying the equation:
x^2 + x^2 + 4x + 4 + x^2 + 8x + 16 = 1460
3x^2 + 12x + 20 = 1460
3x^2 + 12x - 1440 = 0
We can solve this quadratic equation by factoring or using the quadratic formula. The factored form is:
(3x-60)(x+24) = 0
So, x = 20 or x = -24. Since we are looking for natural numbers, we choose x = 20. Hence, the three numbers are 20, 22, and 24.
Therefore, the answer is (b) 20, 22, 24.