Question

Please solve question 25
No spamming please

Answer 1

Answer:

OPTION THREE

Step-by-step explanation:

Option One equals 0.05

Option Two equals -0.05

Option Three equals 0.0098

Option Four equals -0.278

We could eliminate option 2 and four because the question asks for a positive number.

And the small positive number is option 3.

Answer 2

Answer:

Option(3)

Step-by-step explanation:

25.

(1)

$Given:10 - 3\sqrt{11}$

$\Longrightarrow10 - 3\sqrt{11} * \frac{10 + 3\sqrt{11}}{10 + 3\sqrt{11}}$

$\Longrightarrow\frac{(10-3\sqrt11)(10 + 3\sqrt{11})}{(10 + 3\sqrt{11})}$

$\Longrightarrow\frac{(10)^2 - (3\sqrt{11})^2}{10+3\sqrt11}$

$\Longrightarrow\frac{1}{10+3\sqrt11}$

(ii)

Given:$\Longrightarrow3\sqrt{11} - 10 * \frac{3\sqrt{11} + 10}{3\sqrt{11} + 10}$

$\Longrightarrow \frac{(3\sqrt{11} - 10)(3\sqrt{11}+10)}{(3\sqrt{11}+10)}$

$\Longrightarrow-\frac{1}{3\sqrt{11}+10}$

(iii)

$Given: 51 - 10\sqrt{26}$

$\Longrightarrow51-10\sqrt{26}*\frac{51+10\sqrt{26}}{ 51 + 10\sqrt{26} }$

$\Longrightarrow\frac{(51-10\sqrt{26})(51 + 10\sqrt{26} )}{51 + 10\sqrt{26}}$

$\Longrightarrow\frac{2601-2600}{51+10\sqrt{26}}$

$\Longrightarrow\frac{1}{51+10\sqrt{26}}$

(iv)

$Given:18 - 5\sqrt{13}$

$\Longrightarrow18 - 5\sqrt{13}*\frac{18+5\sqrt{13}}{18+5\sqrt{13}}$

$\Longrightarrow\frac{(18 - 5\sqrt{13})(18 + 5\sqrt{13})}{18 + 5\sqrt{13}}$

$\Longrightarrow-\frac{1}{18+5\sqrt{13} }$

From (i),(ii),(iii),(iv)

Only (i) & (iii) can be considered because those are positive.

$\Longrightarrow\boxed{\frac{1}{10+3\sqrt{11}}} > \boxed{\frac{1}{51+10\sqrt{26}}}$

Hope it helps!