Question

FULL SOLUTION
#BRAINLY STARS
#MODERATORS

find the value of (a) and (b)
$\frac{6}{3 \sqrt{2} + 2 \sqrt{3} } + \frac{6}{3 \sqrt{2} - 2 \sqrt{3} } = a \sqrt{2} + b$

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Answer 1

6/(3√2+2√3) +6/(3√2-2√3) = a√2+b

In LHS, take LCM

= 6(3√2-2√3) +6(3√2+2√3)

(3√2+2√3) (3√2-2√3)

= 18√2 - 12√3 + 18√2 + 12√3

(3√2)²-(2√3)²

= 36√2.

9×2 - 4×3

= 36√2.

18 - 12

= 36√2

6

= 6√2

compare this term with RHS

we get

6√2 +0 = a√2 + b

i.e. a=6 or b=0

Thus, the value of a and b is 6 or 0 respectively.

Answer 2

∫Cδ(ζ(z))⋅(1−I(Re(z)−1/2))⋅(1−I(Im(z)))∫Cδ(ζ(z))⋅(1−I(Re(z)−1/2))⋅(1−I(Im(z)))dzdz

where δδ is the impulse “function” and I(x)=1I(x)=1 if x=0x=0 and 00 otherwise.

If it's zero, then the Riemann Hypothesis is true.

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Kostyantyn Mazur

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Benjamin Colson

, Freshman in Linear Algebra

Updated Apr 30, 2017

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