Find the value of a and b- if 2 - -52 - 3-5 - a-5 - b

2 √(5)2+3√(5) ⇒(2 √(5))(3√(5) 2)(3√(5)+2)(3√(5) 2) ⇒6√(5) 4 15+2√(5)41 ⇒8√( )1941 ∴ a=841,b= 1941 ...

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Solving a Quadratic Equation by Completion of Squares Method

Find the valu...

Question

Find the value of a and b, if $\frac{2 - \sqrt{5}}{2 + 3 \sqrt{5}} = a \sqrt{5} + b$

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Solution

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a

b .

\frac{2 - \sqrt{5}}{2 + 3 \sqrt{5}} = a \sqrt{5} + b

a

b

\frac{3 - \sqrt{5}}{3 + 2 \sqrt{5}}

= a \sqrt{5} - \frac{b}{11}

A = (5 \sqrt{2} + 6 \sqrt{3}) (4 \sqrt{2} - 5 \sqrt{3})

B = (7 \sqrt{2} + 5 \sqrt{3}) (8 \sqrt{2} - 5 \sqrt{3})

A + B

\frac{3 + \sqrt{5}}{2 \sqrt{5} + 3} = a + b \sqrt{5}

2160 = 2^{a} {.3}^{b} {.5}^{c}

3^{a} {.2}^{- b} {.5}^{- c}

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