How do I prove that \(\displaystyle\sqrt{{{3}}}{\left\lbrace{5}\sqrt{{{2}}}+{7}\right\rbrace}-\sqrt{{{3}}}{\left\lbrace{5}\sqrt{{{2}}}-{7}\right\rbrace}\) is

Henry Winters

Henry Winters

Answered question

2022-04-12

How do I prove that 52+73-52-73 is an integer?

Answer & Explanation

mortaraskxnl

mortaraskxnl

Beginner2022-04-13Added 12 answers

If we numerically calculate 52+73 it looks an awful lot like 1+2 which is a big hint. Let’s prove that first:
(1+2)3=1+32+3(2)2+(2)3=7+52
Similarly,
(1+2)3=1+323(2)2+(2)3=7+52
Now that we have those cube roots in recognizable form, the rest is easy:
52+73-52-73=(1+2)-(-1+2)=2

Kendall Wilkinson

Kendall Wilkinson

Beginner2022-04-14Added 17 answers

x=52+73-52-73
x3=14-3(50-493)x
x3=143x
x3+3x14=0
(x2)(x2+2x+7)=0
Since the discriminant of the second bracket is less than 0, we can ignore it, and continue with
x2=0
x=2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?