induction question (1 Viewer)

[bubblesss]

hey guys,

i had trouble with this induction question in my last assessment task.......could someone please show me the their working out and their approach to this question?
prove by induction,
a^k + b^k < c^k

for k> or = 3
where a, b and c are the sides of a right angled triangle with c being the hypotenuse.

thanks in advance.

 

[Templar]

What is the condition on a,b and c? I could easily come up with a counterexample if there is no additional conditions.

 

[bubblesss]

What is the condition on a,b and c? I could easily come up with a counterexample if there is no additional conditions.

there aren't any conditions....

 

[Templar]

Let a=1, b=2, c=3. Question disproved.

 

[bubblesss]

Let a=1, b=2, c=3. Question disproved.

oops sry
its meant to be a^k + b^k < c^k

my bad..
i think i should type up the whole question...i mixed it up with another question.

 

[lolokay]

wtf@question? a,b,c are...?

 

[bubblesss]

wtf@question? a,b,c are...?

sry sry my bad
ive fixed the question now.

 

[lolokay]

a² + b² = c²
c > a,b

show
a³ + b³ < c³
for starters
should be able to do it with that

 

[bubblesss]

a² + b² = c²
c > a,b

show
a³ + b³ < c³
for starters
should be able to do it with that

sry but how exactly do u show that?
do i have to prove it for k=3?

 

[lolokay]

just think of a way to show that, using what you know (what i put above it)
that should give you the general method for the induction part

 

[bubblesss]

just think of a way to show that, using what you know (what i put above it)
that should give you the general method for the induction part

oh kkz thanks

 

[Trebla]