Math, asked by devuzhome1, 5 hours ago

pls tell a relevant answer.

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Answered by senboni123456
1

Step-by-step explanation:

We have,

x =  \sqrt[3]{ \sqrt{50} + 7 }  -  \sqrt[3]{ \sqrt{50} - 7 }  \\

 \implies \: x^{3}  =   \bigg(\sqrt[3]{ \sqrt{50} + 7 }  -  \sqrt[3]{ \sqrt{50} - 7 }  \bigg) ^{3}   \\

 \implies \: x^{3}  =   \bigg(\sqrt[3]{ \sqrt{50} + 7 }  \bigg)^{3}  - \bigg(  \sqrt[3]{ \sqrt{50} - 7 }  \bigg) ^{3}   - 3 .\bigg(\sqrt[3]{ \sqrt{50} + 7 }  \bigg).\bigg(\sqrt[3]{ \sqrt{50}  -  7 }  \bigg). \bigg(\sqrt[3]{ \sqrt{50} + 7 }  - \sqrt[3]{ \sqrt{50}  -  7 } \bigg) \\

 \implies \: x^{3}  =    \sqrt{50} + 7   - \sqrt{50}  + 7   - 3 .\bigg(\sqrt[3]{50  - 49}  \bigg). (x) \\

 \implies \: x^{3}  =   14   - 3 x \\

 \implies \: x^{3} + 3x - 14  =  0\\

 \implies \: x^{3}  - 2 {x}^{2}  + 2 {x}^{2} - 4x + 7x- 14  =  0\\

 \implies \: x^{2}(x  - 2)   + 2 x(x- 2)+ 7(x- 2) =  0\\

 \implies \: (x  - 2)( {x}^{2}    + 2 x+ 7) =  0\\

 \implies \: (x  - 2) = 0 \:  \: or \:  \: ( {x}^{2}    + 2 x+ 7) =  0\\

But x²+2x+7 is always positive because its a>0 and D<0

So, x=2

Which implies x^{4}=(2)^{4}=16

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