Let a, b, c, d be real numbers between -5 and | vedclass

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Question

(a)

Given,

$|a|=\sqrt{4-\sqrt{5-a}}$

$|b|=\sqrt{4+\sqrt{5-b}}$

$|c|=\sqrt{4-\sqrt{5+c}}$

$|d|=\sqrt{4+\sqrt{5+d}}$

On squaring, we g

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(a)

Given,

$|a|=\sqrt{4-\sqrt{5-a}}$

$|b|=\sqrt{4+\sqrt{5-b}}$

$|c|=\sqrt{4-\sqrt{5+c}}$

$|d|=\sqrt{4+\sqrt{5+d}}$

On squaring, we get

$a^2=4-\sqrt{5-a}$

$=a^2-4=-\sqrt{5-a}$

Again squaring, we get

$a^4-8 a^2+16=5-a$

$a^4-8 a^2+a+11=0$

Similarly, squaring other given equation and solving we can say that $a, b,-c,-d$ are roots of equation

$x^4-8 x^2+x+11=0$

$	herefore$ The product of roots

i.e. $a b c d=11$

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 $a b c d$ is

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