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i ve get the eqn for tangent plane?

\[1/2[1/\sqrt{p} +1/\sqrt{q}+1/\sqrt{r}]=0\]

yes, now dot that with a general vector in the plane to get the equation of the tangent plane

\[1/2{p/\sqrt{p}(x-p) + q/\sqrt{q}(y-q) +r/\sqrt{r}(z-r)} =0\]

how to simplify?

ok.

hw to get the second eqn?

ok!

now plug in for each intercept
x=0, y=0, z=0
add the three results, what do you get?

what happened to the 1/2 for the dot product?

all that stuff was =0, so multiplying both sides by 2 it is still =0, but simpler

k. hw do i sub for each intercept?

is it (x, y,z) =1 respectively

x=0 will give you one equation, y=0 another, z=0 another
add them all up

sorry, I guess I mean xy=0, yz=0, xz=0

im stuck

to find the x-intercept, plug in y=0 and z=0
what do you get?

r −1/2 z=p 1/2 +q 1/2 +r 1/2

you plugged in x=0 and y=0, so this is going to be the z-intercept
solve for z

z= 1

how do you get that?

r −1/2 z=r 1/2

where did p and q go?

besides, what you wrote would imply that z=r

as x and y is 0

show me an eg

but x and y being zero does not change the value of p and q

the x-intercept *of the plane* will be found by plugging in y=z=0 to our formula *for the plane*

sorry, typo\[p^{-1/2}x=p^{1/2}+q^{1/2}+r^{1/2}\implies x=p+p^{1/2}q^{1/2}+p^{1/2}r^{1/2}\]

q −1/2 y=p 1/2 +q 1/2 +r 1/2 ⟹y=p1/2q1q+p 1/2 r 1/2

how to solve for the unknowns?

so get the z-intercept, then add the x, y, and z-intercept together

hw to get the sum?

just add them; it will look ugly at first, but a miracle will happen...

erm, just add the intercepts...

eg?

this looks ugly, but it can be factored
look at the original function... what is the relationship?

sry nt sure

wow hw do do this?

to do what?

simplify hw?

how did I know the above you mean? practice and recognizing forms

do you see what to do from here at all?

no.pls

remember that p, q, and r satisfy our original equation, so\[\sqrt p+\sqrt q+\sqrt r=\sqrt c\]

how to get simplified to (p √ +q √ +r √ ) 2 ?

ok .thanks a lot!!!!!

welcome, this was a good mental exercise to start my day :)