Poland Junior Math Olympiad Question | 2 Different Methods

Poland Junior Math Olympiad Question | 2 Different Methods

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[caioalmeida]

There's also a 3rd method, which is by doing x := sinh²(t); leading to e^t = 11, thus x = (11 - 1/11)²/4.
Also, thanks for sharing the question!

[AdityaKumar-iypu]

I solve it in the following way
√(x + 1) + √x = 11
= √(x + 1) = (11 - √x)
By squaring both sides, we get
x + 1 = 121 + x - 22√x
= 22√x = 121 - 1 + x - x
= 22√x = 120 = √x = 60/11
Hence, x = 3600/121

[suganyas]

In pair of linear equation in two variables, why do we have the condition a^2 +b^2≠0

[abm]

I always use conjugate method when i deal with problems like this

[walterwen]

Olympiad Question: sqrt(x) + sqrt(x + 1) = 11; x = ?
sqrt(x + 1) = 11 – sqrt(x), x + 1 = [11 – sqrt(x)]^2 = 11^2 – 22sqrt(x) + x
22sqrt(x) = 120, sqrt(x) = 60/11; x = (60/11)^2