Question

simplify 1/2+√5 + 1/√5+√6 + 1/√6+√7 + 1/√7+√8 + 1/√8+√9

( don't give unnecessary answers ) ( give correct answer only )​

Answer 1

$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star QUESTION ::}}}\mid}}}\end{gathered}$

simplify 1/2+√5 + 1/√5+√6 + 1/√6+√7 + 1/√7+√8 + 1/√8+√9

$\huge\mathfrak\pink{answer}$

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$\frac{1}{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } \\ \\ \frac{2 - \sqrt{5} }{4 - 5} - 2 + \sqrt{5}$

$\frac{1}{ \sqrt{5} + \sqrt{6} } = \frac{ \sqrt{5} - \sqrt{6} }{ \sqrt{5} - \sqrt{6} } \\ \\ = \frac{ \sqrt{5} - \sqrt{6} }{5 - 6} \\ \\ = - \sqrt{5 } + \sqrt{6}$

$\frac{1}{ \sqrt{6} + \sqrt{7} } = \frac{ \sqrt{6} - \sqrt{7} }{ \sqrt{6} - \sqrt{7} } \\ \\ = \frac{ \sqrt{6} - \sqrt{7} }{6 - 7} \\ \\ = - \sqrt{6} + \sqrt{7}$

$\frac{1}{ \sqrt{7} + \sqrt{8} } \times \frac{ \sqrt{7} - \sqrt{8} }{ \sqrt{7} - \sqrt{8} } \\ \\ \frac{ \sqrt{7} - \sqrt{8} }{7 - 8} = - \sqrt{7} + \sqrt{8}$

$\frac{1}{ \sqrt{8} + \sqrt{9} } = \frac{ \sqrt{8} - \sqrt{9} }{ \sqrt{8} - \sqrt{9} } \\ \\ = \frac{ \sqrt{8} - \sqrt{9} }{8 - 9} \\ \\ = - \sqrt{8} + \sqrt{9}$

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now, simplify all by cancelling..

u will get the remaining as:

$- 2 + \sqrt{9} \\ \\ = - 2 + 3 \\ \\ + 1 \: or \: 1$

hence your answer is

$\Large\orange{\textbf {\textsf {1}}}$

hope its helpful⭐✨

$\huge\sf\underline\red{answered\:by\:KIMU}$

Answer 2

Given:

Age of both is In ratio 5:7

To Assume:

Their Present Age

Formula Used:

\begin{gathered}( - )+ ( - ) = (+) \\ ( + ) + ( - ) = ( - ) \\ ( + ) + ( + ) = ( + ) \\ ( - ) + ( + ) = ( - )\end{gathered}

(−)+(−)=(+)

(+)+(−)=(−)

(+)+(+)=(+)

(−)+(+)=(−)

Solution:

Let the age of

Rahul be 5x

Haroon age 7x

Equation:

5x - 4 + 7x + 4 = 565x−4+7x+4=56

\color{crimson}{5x}5x - \color{hotpink}{4}4 + \color{crimson}{7x}7x + \color{hotpink}{4}4 = 56

12x + \color{hotpink}{8}8 =56

12x = \color{crimson}{56-8}56−8

\color{hotpink}{12}12 x=\color{hotpink}{48}48

X = \color{crimson}{48/12}48/12

X=\color{hotpink}{4}4

Age of Rahul=5x=5(4)= \color{hotpink}{20years}20years

Age of Haroon=7x=7(4)= \color{hotpink}{28years}28years

∴The Present age of Rahul is 20 And Haroon is 28.