Question

please answer all these quetions in a need

Answer 1

$\bold{\boxed{10.}}$

a = (2 + √3)

a² = (4 + 3 + 4√3)

a² = (7 + 4√3)---------------( 1 )

1/a² = 1/(7 + 4√3) * (7 - 4√3)/(7 - 4√3)

1/a² = (7 - 4√3)/(49 - 48)

1/a² = (7 - 4√3)-------------( 2 )

adding---------( 1 ) & --------( 2 )

a² + 1/a² = (7 + 4√3) + (7 - 4√3)

(a² + 1/a²) = 7 + 7 + 4√3 - 4√3

(a² + 1/a²) = 14

$\bold{\boxed{11.}}$ $\bold{\frac{\sqrt{2} + 2\sqrt{3}}{2\sqrt{2} + \sqrt{3}}}$ = a + b√6

solving L.H.S

$\bold{\frac{\sqrt{2} + 2\sqrt{3}}{2\sqrt{2} + \sqrt{3}}}$ * $\bold{\frac{2\sqrt{2} - \sqrt{3}}{2\sqrt{2} - \sqrt{3}}}$

$\bold{\frac{4 - \sqrt{6} + 4\sqrt{6} - 6}{8 - 3}}$$\bold{\frac{3\sqrt{6} - 2}{5}}$

Comparing with R.H.S

a = (-2/5) , b = 3/5

$\bold{\boxed{12.}}$ $\bold{\frac{3\sqrt{2} + 2\sqrt{3}}{5\sqrt{2} - 4\sqrt{3}}}$ = a - b√6

Solving L.H.S

$\bold{\frac{3\sqrt{2} + 2\sqrt{3}}{5\sqrt{2} - 4\sqrt{3}}}$ * $\bold{\frac{5\sqrt{2} + 4\sqrt{3}}{5\sqrt{2} + 4\sqrt{3}}}$

$\bold{\frac{30 + 12\sqrt{6} + 10\sqrt{6} + 24}{50 - 48}}$

$\bold{\frac{54 + 22\sqrt{6}}{2}}$

ON comparing with R.H.S,

a = 54/2 , -b = -22/2a = 27 , -b = -11

$\bold{\boxed{13.}}$

( a ) (64/25)^(-3/2)

(25/64)^(3/2) = [ (5/8)² ]^(3/2)

(5/8)$\bold{^{2*3/2}}$ = (5/8)³

(125/512)

( b ) (0.00032)$\bold{^{-2/5}}$

(32/100000)$\bold{^{-2/5}}$

$\bold{[(10)^5/(2)^5]^{2/5}}$

$\bold{(10/2)^2}$

$\bold{100/4}$

( C ) $\bold{(81/16)^{-3/4} * (25/9)^{-3/2} * (2/5)^{-3}}$

$\bold{[(2/3)^4]^{3/4} * [(3/5)^2]^{3/2} * (5/2)^3}$

$\bold{(8/27) * (27/125) * (125/8)}$

$\bold{1}$

Answer 2

$\bf{hey}$
$\bf \underline{here \: is \: the \: answer}$
⬇⤵⬇⤵⬇⤵❕

this refers to the pic.

$\underline{hope \: it \: helps}$
$\boxed{thanks}$