perplexus.info :: Just Math : Nested Radical Product

Nested Radical Product (Posted on 2025-03-05)

If

a = √(4 - √(5 - a))
b = √(4 + √(5 - b))
c = √(4 - √(5 + c))
d = √(4 + √(5 + d))

Determine the value of the product abcd.

No Solution Yet Submitted by Danish Ahmed Khan

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computer solution

| Comment 2 of 4 |

syms x

eq=x==sqrt(4-sqrt(5-x));

a=vpasolve(eq)

eq=x==sqrt(4+sqrt(5-x));

b=vpasolve(eq)

eq=x==sqrt(4-sqrt(5+x));

c=vpasolve(eq)

eq=x==sqrt(4+sqrt(5+x));

d=vpasolve(eq)

a*b*c*d

>> nestedRadicalProduct

a =

1.4550597321528548939400134829319

b =

2.3709560684852830466809098114235

c =

1.2266515629061599104616873607251

d =

2.5993642377319780301592359336303

ans =

11.0

Posted by Charlie on 2025-03-05 14:54:56

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