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10)( a+ 1/a)^2 = a^2 + 1/a^2 + 2
= 23 + 2
= 25
a + 1/a = +-5
11)( x -1/x)^2 = x^2 + 1/x^2 - 2
= 51 -2 = 49
x- 1/x = +-7
12)( 2.3)^2 - ( 0.3)^2)/ ( 2.3- 0.3)^2
= ( 2.3 + 0.3) ( 2.3 -0.3) / ( 2.3 - 0.3)^2
= ( 2.6) / ( 2)
= 13/10 = 1.3
13)3x - 4y = 10
xy = -1
( 3x -4y)^2 = 100
9x ^2 + 16 y^2 - 24 xy = 100
9 x^2 + 16 y^2 + 24 =100
9 x^2 + 16 y^2 = 76
14)5x - 2y = 7
xy = 2
(5x -2y)^2= 25x^2 + 4y^2 - 20 xy = 49
25 x^2 + 4y^2 - 40= 49
25 x^2 + 4y^2 = 89
( 5x +2y)^2 = 25 x^2 + 4y^2 + 20xy
= 89 + 40= 139
15) a + 1/a = 17/4
( a+ 1/a)^2 = ( 17/4)^2 = 289/16
a^2 + 1/a^2 + 2 = 289/16
a^2 + 1/a^2 = 289/16 - 2 = 289 - 32)/ 16
= 257/16
( a-1/a)^2 = a^2 + 1/a^2 -2
= 257/16 -2
= 257 - 32)/ 16 = 225/16
a- 1/a = 15/4
= 23 + 2
= 25
a + 1/a = +-5
11)( x -1/x)^2 = x^2 + 1/x^2 - 2
= 51 -2 = 49
x- 1/x = +-7
12)( 2.3)^2 - ( 0.3)^2)/ ( 2.3- 0.3)^2
= ( 2.3 + 0.3) ( 2.3 -0.3) / ( 2.3 - 0.3)^2
= ( 2.6) / ( 2)
= 13/10 = 1.3
13)3x - 4y = 10
xy = -1
( 3x -4y)^2 = 100
9x ^2 + 16 y^2 - 24 xy = 100
9 x^2 + 16 y^2 + 24 =100
9 x^2 + 16 y^2 = 76
14)5x - 2y = 7
xy = 2
(5x -2y)^2= 25x^2 + 4y^2 - 20 xy = 49
25 x^2 + 4y^2 - 40= 49
25 x^2 + 4y^2 = 89
( 5x +2y)^2 = 25 x^2 + 4y^2 + 20xy
= 89 + 40= 139
15) a + 1/a = 17/4
( a+ 1/a)^2 = ( 17/4)^2 = 289/16
a^2 + 1/a^2 + 2 = 289/16
a^2 + 1/a^2 = 289/16 - 2 = 289 - 32)/ 16
= 257/16
( a-1/a)^2 = a^2 + 1/a^2 -2
= 257/16 -2
= 257 - 32)/ 16 = 225/16
a- 1/a = 15/4
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