Tommorow is my exam .plz give me answers of these questions.

1] if  X+Y =8 and XY =15,find Xraise to power of 2 + Y raise to power of 2.

2] if  X = 3 -2*root 2,then find value of  X raise to power of 2 -1/X raise to power of 2.

1=

x+y=8

xy=15 find x2+y2

using the identity

(x+y)2 = x2 +y2+2xy

putting the values

82=x2+y2+2*15

64=x2+y2+30

x2+y2=64-30=34

ans=34

 

2=

x=3-2√2   find x2-1/x2

1/x=1/3-2√2    

1/x=1/3-2√2 *3+2√2/3+2√2         Rationalising the denominator 

3+2√2

putting the values

(3-2√2)2-(3+2√2)2

(9+8-2*3*2√2)-(9+8+2*3*2√2)        (((( a2+b2+2ab and a2+b2-2ab)))))

(17-12√2)-(17+12√2)

17-12√2-17-12√2

-24√2

ans=-24√2

Hope this helps

  • 2

[1]

We have,

X + Y = 8 

By squaring both the sides,

(X + Y)2 =8

X2 + 2XY + Y2 = 64 

X2 + Y2 + 2(15) = 64

X2 + Y2 + 30 = 64

X2 + Y2 = 64-30

X2 + Y2 = 34

  • 0

[2]

We have,

X = 3-22  

X2 = (3-2

)2

 

X2 = 32 - 2*3*2

2 + (2

2)2

 

 

 

X2 = 9 - 122 + 8

X2 = 17 - 122

 

1/X2 = 1/17-122

1/X2  = 1 / 17-122 * 17+122 / 17+122

1/X2 = 17+122 / (17)2 - (12

2)2

 

1/X2 = 17+122 / 1 

1/X2 = 17 + 122

 

 

X2 + 1/X2 = 17- 122 +17 +122

X2 + 1/X2 = 17 + 17

X2 + 1/X2 = 34

 

 

Hope this helps!!!!

 

 

 

  • -1
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