Find a-b-c- 1 7-4- 3 - 1 2- 5 - a-b- 3 - c

=1/7+4√(3)+1/√(5)+2 =7 4√(3)/(7+4√(3))(7 4√(3))+√(5) 2/(√(5) 2)(√(5)+2) =7 4√(3)/7^2 (4√(3))^2+√(5) 2/(√(5))^2 2^2 as (a+b)(a b)=a^2 b^2 ...

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Byju's Answer

Standard XII

Mathematics

Vn Method

Find a+b+c,...

Question

Find $a + b + c$ , $\frac{1}{7 + 4 \sqrt{3}} + \frac{1}{2 + \sqrt{5}}$ = $a - b \sqrt{3} + \sqrt{c}$

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Solution

$= \frac{1}{7 + 4 \sqrt{3}} + \frac{1}{\sqrt{5} + 2}$

$= \frac{7 - 4 \sqrt{3}}{(7 + 4 \sqrt{3}) (7 - 4 \sqrt{3})} + \frac{\sqrt{5} - 2}{(\sqrt{5} - 2) (\sqrt{5} + 2)}$

$= \frac{7 - 4 \sqrt{3}}{7^{2} - (4 \sqrt{3})^{2}} + \frac{\sqrt{5} - 2}{(\sqrt{5})^{2} - 2^{2}}$

as $(a + b) (a - b) = a^{2} - b^{2}$

$= \frac{7 - 4 \sqrt{3}}{49 - 48} + \frac{\sqrt{5} - 2}{5 - 4}$

$= 7 - 4 \sqrt{3} + \sqrt{5} - 2 = 5 - 4 \sqrt{3} + \sqrt{5}$

comparing with $a - b \sqrt{3} + \sqrt{c},$
we get,
$a = 5, b = 4, c = 5$

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Similar questions

Q. Find

a : c

when

(1) a : b = 2 : 5

and

b : c = 4 : 7

(2) a : b = 1 \frac{1}{2} : 1 \frac{2}{3}

and

b : c = 1 \frac{2}{3} : 5

Q. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8}. Find A ∪ B ∪ C.

If
A = {1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

C = {6, 7, 8, 9}

D = {7, 8, 9, 10}

$\begin{matrix} C o l u m n A & C o l u m n B 1. A \cup B & a . {3, 4, 6, 7} 2. A \cap B & b . \emptyset 3. (B \cap C) \cup D & c . {3, 4} 4. B \cup C \cup D & d . {3, 4, 5, 6, 7, 8, 9, 10} 5. (A \cap B) \cap (B \cup C) & e . {1, 2, 3, 4, 5, 6, 7} f . {6, 7, 8, 9, 10} g . {7} \end{matrix}$

Find:

(i) of (a) (b) (c)

(ii) of (a) (b) (c)

Q. If universal set U = {0, 1, 2, 3, 4, 5, 6, 7}
A = (2, 3, 7}, B = {4, 6} and C = {0, 2, 4, 6}.
Find B′ ∩ C′ .

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Find a+b+c, 17+4√3+12+√5=a−b√3+√c

=17+4√3+1√5+2=7−4√3(7+4√3)(7−4√3)+√5−2(√5−2)(√5+2)=7−4√372−(4√3)2+√5−2(√5)2−22as (a+b)(a−b)=a2−b2=7−4√349−48+√5−25−4=7−4√3+√5−2=5−4√3+√5comparing with a−b√3+√c,we get,a=5,b=4,c=5

Find $a + b + c$ , $\frac{1}{7 + 4 \sqrt{3}} + \frac{1}{2 + \sqrt{5}}$ = $a - b \sqrt{3} + \sqrt{c}$