minhthien2016

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7 years, 306 days

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These are questions asked by minhthien2016

This is my code
 

restart;
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [a, 0, 0];
C := [a, a, 0];
DD := [0, a, 0];
S := [0, 0, h];
d1 := Line(A, C);
d2 := Line(S, DD);
(Distance(d1, d2) assuming (a::positive and h::positive));

I got 

abs(a)^2*abs(h)/sqrt(2*abs(a*h)^2 + abs(a)^4)

How can I remove abs?

How can I find a relation of a, b, c, d, t (a d <> 0) so that the function f(x) = (a x^2 + b x + c)/(d x +t) is a increasing function on the interval (m, n)? I know that, we have the conditions 
f'(x) >=0 forall x in (m, n) and -t/d not in (m, n)

Let SABCD be a pyramid, with the line SA perpendicular to the plane ABCABCD is a rectangle, AB = aAB = bSA = hH is projection point of A on the line SC and K is projection point of A on the line SD. How can I find radius of the circumcircle of triangle CHK?

restart;
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [a, 0, 0];
C := [a, b, 0];
DD := [0, b, 0];
S := [0, 0, h];
lineSC := Line(S, C);
lineSD := Line(S, DD);
H := Projection(A, lineSC);
K := Projection(A, lineSD);

My code
restart;
reqn:=f(n+1) = f(n)  + sqrt(2*f(n+1)-f(n)):
rsolve({reqn, f(1) = 15},f(n));

I can not get the answer. How can I get the answer?

I am trying to find the integer numbers a, b, c, d, t so that the equation sqrt(a x^2 + b x + c) = d x + t have two integer solutions. My code

First I solve

solve(a*x^2 + b*x + c = (d*x + t)^2, x);

I get

(2*d*t - b + sqrt(4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2))/(2*(-d^2 + a)), -(-2*d*t + sqrt(4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2) + b)/(2*(-d^2 + a))

And then, I solve
restart;
n := 0;
for a to 10 do
for b to 10 do
for c to 10 do
for d to 10 do
for t to 10 do
mydelta := 4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2;
if 0 < mydelta and type(mydelta, integer) then
x1 := (2*d*t - b + sqrt(4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2))/(2*(-d^2 + a));
x2 := -(-2*d*t + sqrt(4*a*t^2 - 4*b*d*t + 4*c*d^2 - 4*a*c + b^2) + b)/(2*(-d^2 + a));
if 0 < d*x1 + t and 0 < d*x2 + t and type(x1, integer) and type(x2, integer) and nops({a, b, c, d, t}) = 5 and c <> t^2 and -d^2 + a <> 0 and nops({x1, x2}) = 2 then n := n + 1; L[n] := [a, b, c, d, t]; end if; end if; end do; end do; end do; end do;
end do;
L := convert(L, list);
nops(L);

I don't get any solutions. But, when I  solve(sqrt(2*x^2 + 3*x + 5) = x + 9, x); I get two solutions 19, -4.
Where is wrong in my code?
 

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