Doubt-3

Solve in real numbers the equation below.

$(1019-x)^{1/2} - (2019 + x)^{1/3} = 16$

Can someone give a method to solve this question or a similar question. Thanks!

#Algebra

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Let (1019-x)^(1/2)=P and second term be Q. Then you have, P-Q=16. P^2+Q^3=3038 =>Q^3+(Q+16)^2=3038. So, you have a cubic equation in Q, which has only one real root, 13. Hence x=178.

Kushal Dey - 1 year, 2 months ago

Thanks. Nice explanation!

Nitin Kumar - 1 year, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$