Question

Find the set of values of y for which
y^2(y^2-5)>36

Answer 1

try distributing (multiplying) the y^2 at the front across the parenthesis...

In other words, simplify the expression first.

Answer 2

Or, never mind... don't do that

Answer 3

ok, let me start over :)

Simplify the left side of the equation by multiplying...

then subtract 36 from both sides to get -36 on the left.

Then you can factor the expression on the left.

Answer 4

y^4-5y^2-36>0??

Answer 5

yes :)

Then you can factor... just think if it was y^2 - 5y - 36.... you'd factor as (y-9)(y+4)

So this is the same, but you have y^4 and y^2 terms instead of y^2 and y

Answer 6

I get (y^2 - 9)(y^2 + 4) > 0

So y^2 - 9 must be greater than 0
and
y^2 + 4 must be greater than 0

...or else both must be less than zero so their product multiplies to be positive.

Answer 7

you need y > 3 or y < -3...

then y^2 will be greater than 9 making the first parenthesis positive, and the second parenthesis will still be positive, so the inequality is still true.

Answer 8

Yes.

Answer 9

How did you factor

y^4-5y^2-36>0

Answer 10

Yes.

Answer 11

try this... it will seem like a trick, but that's ok...

let some other variable by equal to y^2... let's call it "b"... so b = y^2

Answer 12

then let's rewrite the expression we are trying to factor using b in place of y^2

b^2 - 5b - 36

Answer 13

at that point, I thought to myself, what factors can you multiply to get 36?

6 and 6, but then the middle term would be -5b
12 and 3... same problem
hey... 9 and 4 work, if the signs are correct...

b^2 - 5b - 36 = (b - 9)(b + 4)

Answer 14

is that making sense so far?

After factoring the easier looking expression using b, then you can just put the y^2 back in, replacing the b terms in the factored expression...

(b - 9)(b + 4) --->>> (y^2 - 9)(y^2 + 4)

Answer 15

Sort of just one question

Answer 16

ok :)

Answer 17

@Hollywood_chrissy what was your question?

Answer 18

You said let y^2=b. But when you set up the expression you had a b^2.

Answer 19

yes, that's because the original expression had a y^4 term... so b = y^2 isn't enough

y^4 = (y^2)(y^2) = (b)(b) = b^2

Answer 20

Ok cool

Answer 21

glad to help :)

Answer 22

You said let y^2=b. But when you set up the expression you had a b^2.