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

Options

A. 11
B. -11
C. 121
D. -121

Answer

A

Explanation

`"Given "|a| =sqrt(4-sqrt(5-a))`
`"squaring"`
`a^(2)=4-sqrt(5-a)`
`rArra^(4)+16-8a^(2)=5-a`
`rArra^(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`
`therefore "product of roots "`
ab(-c)(-d)=11
abcd=11