Discussion Room : Quant

SOLVE
(X^4+X^2+1)/(X^24X5) < 0SOLVE
(X^2+6X7)/(X^2 + 1)

N = 2³ * 5³ * 7², how many sets of two factors of N are coprime

@vinaycat2017 45:72:80
19778800
7228800

If F(x) = x^4  360x^2 + 400 (for any integral value of x) and if F(x) is a prime number, then what is the sum of all possible values of F(x)? Cold anyone help [email protected] sir please help.


find the maximum value of n such that
42×57×92×91×52×62×63×64×65×66×67 is perfectly divisible by 42*n

@swanandk12 I think it is infinity. As x increases the value of F(x) will keep on increasing. So possible values of F(x) are infinite. Hence the sum of possible values F(x) is infinity. Thoughts?

If 76/(4+√7+√11)=p+q√7+r√11+s√77 then p+q+r+s=?

@rohitchopra01 said in Discussion Room : Quant:
If 76/(4+√7+√11)=p+q√7+r√11+s√77 then p+q+r+s=?
Multiply both sides by (4 + 71/2 + 111/2)
76 = (4 + 71/2 + 111/2)p + 71/2(4 + 71/2 + 111/2)q + 111/2(4 + 71/2 + 111/2)r + 771/2(4 + 71/2 + 111/2)s
Expand out:
76 = 4p + 71/2p + 111/2p + 71/24q + 7q + 771/2q + 111/24r + 771/2r + 11r + 771/24s + 111/27s + 71/211sNow get everything together:
76 = (4p+7q+11r) + 71/2(p+4q+11s) + 111/2(p+4r+7s) + 771/2(q+r+4s)Rewrite the LHS:
76 + 0 * 71/2 + 0 * 111/2 + 0 * 771/2 = (4p+7q+11r) + 71/2(p+4q+11s) + 111/2(p+4r+7s) + 771/2(q+r+4s)So we have the following system of equations:
4p + 7q + 11r = 76
p + 4q + 11s = 0
p + 4r + 7s = 0
q + r + 4s = 04 equations in 4 unknowns. Solve.

Find sum of
√{5+√[11+√【19+√(29..........To infinity