Let a, b, c, d be real numbers between -5 and 5 such that |a|=√{4-√{5-a}},|b|=√{4+

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4-2.Quadratic Equations and Inequations

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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

$11$

$-11$

$121$

$-121$

(KVPY-2017)

Solution

(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

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

$\therefore$ The product of roots

i.e. $a b c d=11$

Standard 11

Mathematics

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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

Solution

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