Mathematics
The sum of the squares of three consecutive even numbers is 596. Find the numbers.
Quadratic Equations
22 Likes
Answer
Let the three consecutive even numbers be represented as x, x + 2, and x + 4.
Given,
The sum of their squares is 596.
⇒ x2 + (x + 2)2 + (x + 4)2 = 596
⇒ x2 + x2 + 4x + 4 + x2 + 8x + 16 = 596
⇒ 3x2 + 12x + 20 = 596
⇒ 3x2 + 12x + 20 - 596 = 0
⇒ 3x2 + 12x - 576 = 0
⇒ 3(x2 + 4x − 192) = 0
⇒ x2 + 4x − 192 = 0
⇒ x2 + 16x - 12x − 192 = 0
⇒ x(x + 16) - 12(x + 16) = 0
⇒ (x - 12)(x + 16) = 0
⇒ (x - 12) = 0 or (x + 16) = 0 [Using zero product rule]
⇒ x = 12 or x = -16.
Case 1 : x = 12
The three consecutive even numbers are:
⇒ x = 12
⇒ x + 2 = 12 + 2 = 14
⇒ x + 4 = 12 + 4 = 16
Case 2: x = −16
The three consecutive even numbers are:
⇒ x = −16
⇒ x + 2 = −16 + 2 = −14
⇒ x + 4 = −16 + 4 = −12
Hence, the two possible sets of three consecutive even numbers are 12, 14, 16 and -16, -14, -12.
Answered By
11 Likes
Related Questions
An arithmetic progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
The roots of the equation (q - r)x2 + (r - p)x + (p - q) = 0 are equal.
Prove that : 2q = p + r, that is, p, q and r are in A.P.
Given matrix, X = prove that X2 = 4X + 5I.
Use a graph sheet for this question. Take 1 cm = 1 unit along both the x and y axis. Plot ABCDE, where A(4, 0), B(4, 2), C(2, 2), D(2, 4) and E(0, 4).
(a) Reflect the points A, B, C and D on the y-axis and name them as F, G, H and I respectively.
(b) Join the points A, B, C, D, E, I, H, G and F in order. Reflect the figure ABCDEIHGF on the x-axis and name it as AMNPQRSTF.
(c) Give the geometrical name of the closed figure AEFQ.