Question

and this tooo plssssss......

Answer 1

Here is your answer

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Answer 2

Heya..!!!


√[ 5 + 2√6] + √ [ 8 - 2√15 ]


we know that:-

(√a + √b)² = a + b + 2√ab

Now,

√(5 + 2√6). If it is a perfect square

On comparing ,

We get,

a + b = 5----(1)
AND,

2√ab = 2√6

⇒ab = 6-----(2)

we know that:-

(a - b)² = (a + b)² - 4ab

⇒ (a - b)² = 5² - 4×6

⇒(a - b)² = 25 - 24

⇒(a - b)² = 1

⇒(a - b) = 1 ---------(3)


from------(1) and------(3)

we get,

a + b =5
a - b = 1
-------------
2a = 6

⇒a = 3 put in---(3)

we get,

a × b = 6

⇒b = 6/2

⇒b = 3 , a = 2


so that, 5 + 2√6 = 3+2+2√(3×2)

=(√3+√2)²

∴ √( 5 + 2√6) = √3+√2.

Similarly,

√(8 - 2√15)

a + b = 8---------(4)

2√ab = 2√15

⇒ab = 15--------(5)

using formula,

(a - b)² = (a + b)² - 4ab

⇒(a - b)² = 8² - 4×15

⇒(a - b)² = 64 - 60

⇒(a - b)² = 4


(a - b) = 2---------(6)


From-----(4) & ------(6)

we get,

a + b = 8
a - b = 2
------------
2a = 10

⇒a = 10/2

⇒a = 5 put in---(5)

we get,

ab = 15

⇒b = 15/5

⇒b = 3 , a = 5



√(8 - 2√15) = (√5 - √3)

∴ √( 5 + 2√6) + √(8 - 2√15) = √3 + √2 + √5 - √3 = √2 + √5.


I HOPE ITS HELP YOU