Exponents and Estimating

[aznmexicana]

Where would one start in solving this??

x^4+ y^4=100 then what is the greatest possible value of x between?

a)0-3 b) 3-6 c) 6-9 d) 9-12 e) 12-15[/list]

[surajgarg]

Where would one start in solving this??

x^4+ y^4=100 then what is the greatest possible value of x between?

a)0-3 b) 3-6 c) 6-9 d) 9-12 e) 12-15[/list]

Its asking for greatest possible value of x.

This is possible when y is least.

Since the exponent of y is 4, an even number, then y^4 will be positive, so we can fix y = 0.

That leaves x^4 = 100
i.e. x^2 = 10
i.e. x = 3.16

So answer is B.

[taneja.niks]

Since the exponent of y is 4, an even number, then we can fix y = 0

what makes u say this statement tht exponent is 4 so its a even number 3^4 is 81 is it a even number????


Please post the answer for the same........

[surajgarg]

Since the exponent of y is 4, an even number, then we can fix y = 0

what makes u say this statement tht exponent is 4 so its a even number 3^4 is 81 is it a even number????


Please post the answer for the same........

Hey niks,

Thanks for the observation. I missed adding a phrase there. I have corrected my post above.

[VS2013]

For the greatest possible value of x, y^4 must be 0.
Therefore, x^4=100= 10*10
Since 3*3=9, then x is slightly greater than 3.
Therefore, answer is b, 3-6.

[zareentaj]

For the greatest possible value of x, y^4 must be 0.
Therefore, x^4=100= 10*10
Since 3*3=9, then x is slightly greater than 3.
Therefore, answer is b, 3-6.

Thank you VS2013.

[arora007]

Where would one start in solving this??

x^4+ y^4=100 then what is the greatest possible value of x between?

a)0-3 b) 3-6 c) 6-9 d) 9-12 e) 12-15[/list]

x^4+ y^4=100

now
x^4+ y^4
= x^4+ y^4 +4(x^2)(y^2) - 4(x^2)(y^2)
=(x^2 +y^2)^2 - (2xy)^2
=(x^2 +y^2 +2xy) (x^2 +y^2 -2xy)
=(x+y)^2 * (x-y)^2
=10^2

so (x+y)(x-y) =10

x^2 -y^2 = 10

x^2 = 10 + y^2

which would mean
x^2 > 10

x > root10
ie. x > 3.16
so b fits....


This seems to be a lenghty way... but I have shown all the steps here.. to make things

people seeing a x^4+ y^4 at once jump to (x+y)^2 * (x-y)^2

the idea in exponent problems always is to try and reduce powers to as manageable as possible...