Let a, b, c, d be real numbers between – 5 and 5 such that |a| =\sqrt{ 4 -\sqrt{5 -a} , |b| = \sqrt{4 + \sqrt{5- b} }, |c| = \sqrt{4 –\sqrt{5 + c} , |d| =\sqrt {4 + \sqrt{5 +d} . Then the product abcd is

KVPY SA Exam 19-Nov-2017 Question Paper

Question : 65 of 80

Marks: +1, -0

Let a, b, c, d be real numbers between – 5 and 5 such that

|a| =√{ 4 -√{5 -a}} ,

|b| = √{4 + √{5- b} },

|c| = √{4 –√{5 + c}} ,

|d| =√ {4 + √{5 +d}} .

Then the product abcd is

Solution:

Given

√{ 4 -√{5 -a}}

squaring

a^2=4-√{5-a}

⇒

a^4 + 16 -8a^2 = 5 -a

⇒

a^4 -8a^2 + a + 11 = 0

Similarly squaring other given equations & solving we can say that a,b, –c, –d are roots of

x^4 -8x^2 + x + 11 = 0

∴ product of roots
ab (–c) (–d) = 11
abcd = 11

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