Question

please answer , as soon as possible​

Answer 1

Answer:

328 answer

Step-by-step explanation:

i thank its help uuuu

Answer 2

Step-by-step explanation:

Given :-

X = √(4-√7) and Y = √(4+√7)

To find :-

Find the value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)²?

Solution :-

Given that:

X = √(4-√7)

It can be written as

On multiplying and dividing by 2 in the squre root

=> X = √[2{(4-√7)}/2]

=> X =√[(8-2√7)/2]

=> X =√[{(7+1)-2√7{/2]

=> X =√[{(√7)²+(√1)²-2(√7)(√1)}/2]

It is in the form of a²-2ab+b²

Where , a = √7 and b = √1

We know that

(a-b)² = a²-2ab+b²

=>X = √[{(√7-√1)}²/2]

=> X = (√7-√1)/√2

=> X = (√7-1)/√2 ----------------(1)

and

Y = √(4+√7)

It can be written as

On multiplying and dividing by 2 in the squre root

=> Y = √[{2(4+√7)}/2]

=> Y =√[(8+2√7)/2]

=> Y =√[{(7+1)+2√7}/2]

=> Y =√[{(√7)²+(√1)²+2(√7)(√1)}/2]

It is in the form of a²+2ab+b²

Where , a = √7 and b = √1

We know that

(a+b)² = a²+2ab+b²

=>Y = √[{(√7+√1)}²/2]

=> Y = (√7+√1)/√2

=> Y = (√7+1 )/√2----------------(2)

On adding (1) &(2)

=> X+Y = (√7-1)/√2+(√7+1)/√2

=>X+Y = (√7-1+√7+1)/√2

=> X+Y = (2√7 )/√2

=> X+Y = (√2×√2×√7)/√2

=> X+Y = √2×√7

=> X+Y = √14--------------(3)

On Subtracting (2) from (1)

=> X-Y =[(√7-1)/√2]-[(√7+1)/√2]

=> X-Y =[ (√7-1 )-(√7+1)]/√2

=> X-Y = (√7-1-√7-1)/√2

=> X-Y = (-1-1)/√2

=> X-Y = -2/√2

=> X-Y = -(√2×√2)/√2

=>X-Y = -√2 -------------------(4)

On multiplying (1)&(2)

=> XY = [(√7-1)/√2][(√7+1)/√2]

=> XY = (√7-1)×(√7+1)/(√2×√2)

=> XY = [(√7)²-(1)²]/(2)

Since (a+b)(a-b) = a²-b²

=> XY = (7-1)/2

=> XY = 6/2

=> XY = 3 -----------------(5)

Now,

The value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)²

It can be written as

=>[(X-Y)²/3] + [ XY(X+Y) ]²+(X+Y)²

From (3),(4)&(5)

=> [(-√2)²/3] + [ 3(√14)]²+(√14)²

=> (2/3) + (9×14)+(14)

=> (2/3)+(126)+(14)

=> (2/3)+140

=> [2+(3×140)]/3

=>(2+420)/3

=> 422/3

Answer:-

The value of [(X-Y)/√3]²+(X²Y+XY²)²+(X+Y)² is 422/3

Used formulae:-

• (a+b)² = a²+2ab+b²

• (a-b)² = a²-2ab+b²

• (a+b)(a-b) = a²-b²