Question

if √13-a√10 = 2√2+√5,then a²+a^-1 is -​

Answer 1

Answer:

+-5√29

step by step explanation:

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supposed to be the right answer in one method,

If a-1/a=5 the a-1=5a

-1=5a-a which is -1=4a which is a=-1/4 ————1

a²-1/a² is (-1/4)² -1/(-1/4)² which is 1/16 -1/1/16.

-15/16 / 1/16

Applying another method from given condition in problem.

Other right answer is a-1/a=5—Eq1

So squaring both sides

We get a² -2a/a +1/a² which is a² +1/a² -2=5×5

Which further is a²+1/a²-2=25—Eq2

Now adding 4 to both sides

a²+1/a²-2+4=25+4

Which is a²+2+1/a²=29

Further square root of both sides

√a²+2+1/a²=√29

a+1/a=√29

Now in problem the then asked what is a²-1/a² is (a+1/a)(a-1/a)

a+1/a ×a-1/a

Whereas in question a-1/a=5 and a+1/a=√29 is proved

So +-5√29 is Answer.

I have one problem with this … problem. It would be much more easily interpreted if there were parentheses. It looks like it could be either:

(a-1)/a = 5

or

a - (1/a) = 5

Very different problems. If it is the former, you can solve for ‘a’ as the other answer states. If it is the later, multiple all terms by ‘a’.

a^2 -1 = 5a

a^2 - 5a - 1 = 0

And at this point, use the quadratic formula to find the two possible values of ‘a’. From there, just plug those values into the other formula.

Still two things to consider:

the other formula may be ambiguous as well

sometimes things that pop out of quadratic may not work in the original equation, or be complex numbers

I hope that helps. Good luck!

Answer 2

Answer:

15.75

Step-by-step explanation:

• √(13-a√10) = 2√2+√5
• (√(13-a√10))² = (√8 +√5 )²
• 13-a√10 = √64 + √25 + 2*√8*√5
• 13-a√10 = 8 + 5 + 2√40
• 13-a√10 = 13 + 4√10
• -a√10 = 4√10
•  a = -4

--------------------------

• a² + a⁻¹ =
• (-4)² + (-4)⁻¹ =
• 16 - 1/4 =
• 15.75