Question

If a, b , c, d are distinct integer such that (x-a) (x-B) (x-c) (x-d) =4 has an integer solution x=r. Find the ratio a+b+c+d/r​

Answer 1

Step-by-step explanation:

The correct option is (d) 1/2 - 1/√2 Explanation: Since. a. h. r are in AP. Let a = A - D, b = A, c = A + D Given, a + b + c = 3/2 Read more on Sarthaks.com - https://www.sarthaks.com/262202/suppose-a-b-c-are-in-ap-and-a-2-b-2-c-2-are-in-gp-if-a-b-c-and-a-b-c-3-2-then-the-value-of-a-is

Answer 2

Given :- If a, b, c and d are distinct integers such that (x-a)(x-b)(x-c)(x-d) = 4 has an integer solution x = r.

To Find :-

• The ratio of (a+b+c+d)/r = ?

Solution :-

→ (x - a) * (x - b) * (x - c) * (x - d) = 4

since a,b,c and d distinct integers ,

→ (x - a) * (x - b) * (x - c) * (x - d) = 1 * (-1) * 2 * (-2) [ note here we can write 1 * (-1) * (-2) * 2 or 2 * 1 * (-2) * (-1) , all have same values .]

comparing we get,

→ x - a = 1 => a = (x - 1)

→ x - b = (-1) => b = (x + 1)

→ x - c = 2 => c = x - 2

→ x - d = (-2) => d = x + 2 .

then,

→ (a + b + c + d)/r

→ (x - 1 + x + 1 + x - 2 + x + 2)/r

→ 4x/r

given that x = r,

therefore,

→ 4r/r

→ 4 .

Hence, the ratio of (a+b+c+d)/r will be (4/1) or we can say that (a + b + c + d) : r = 4 : 1 .

Learn more :-

Let a, b and c be non-zero real numbers satisfying (a³)/(b³ + c³) + (b³)/(c³ + a³) + (c³)/(a³ + b³)

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if a²+ab+b²=25

b²+bc+c²=49

c²+ca+a²=64

Then, find the value of

(a+b+c)² - 100 = __

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