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Algebra Level 2

x 4 = 12 7 − x 4 \large \sqrt[4] x = \dfrac{12}{7 -\sqrt[4] x}

Find the sum of solutions to the equation above.


The answer is 337.

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Anish Harsha by Anish Harsha , 20, India

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1 solution

Rishabh Jain
Mar 23, 2016

Let x 4 = t \color{#D61F06}{\sqrt[4]{x}=t} equation simplifies to: t = 12 7 − t \color{#D61F06}{t}=\dfrac{12}{7-\color{#D61F06}{t}} ⟹ t 2 − 7 t + 12 = 0 \implies \color{#D61F06}{t}^2-7\color{#D61F06}{t}+12=0 ⟹ ( t − 3 ) ( t − 4 ) = 0 \implies (\color{#D61F06}{t}-3)(\color{#D61F06}{t}-4)=0 ⟹ x 4 = t = 3 , 4 \implies \color{#D61F06}{\sqrt[4]{x}}=\color{#D61F06}{t}=3,4 ⟹ x = 4 4 , 3 4 \implies \color{#69047E}{x=4^4,3^4} 4 4 + 3 4 = 337 \huge \color{#69047E}{4^4+3^4=\boxed{337}}

22 Helpful 0 Interesting 0 Brilliant 0 Confused

Great solution as always!

John Frank - 5 years, 2 months ago

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Thanks..... :-)

Rishabh Jain - 5 years, 2 months ago

same way, good solution! +1

Silver Vice - 5 years, 2 months ago

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Great... Thanks.. :-)

Rishabh Jain - 5 years, 2 months ago

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