Question

Q.1)Evaluate the following by using suitable identities:1.)185*185-115*115 2.)if x+1/x=6, find x^2+1/x^2 and x^4+1/x^4. 3.)if x+1/x=7, find x^3+1/x^3. Q.2)Factories following using identities:1.)4√3x^2+5x-2√3. 2.)32a^3+108b^3


pls. answer fast.....

Answer 1

☆Hello friend☆

1) (185×185) - (115×115)

= 185^2 - 115^2

= (185-115)(185+115)

=21000

2) x+1/x = 6

(x+ 1/x)^2 = 6^2

x^2 + (1/x)^2 + (2× x × 1/x)= 36

x^2 + 1/x^2 = 36-2

x^2 + 1/x ^2 = 34

3) Same like second, incontinuation

(x^2 + 1/x^2)^2= 34^2

x^4 + 1/x^4 +(2×x^2×1/x^2)= 1156

x^4 + 1/x^4 = 1156-2

x^4 + 1/x^4 = 1154

$hope \: it \: help$

☺☺☺

Answer 2

Hi ,

1 ) 4√3 x² + 5x - 2√3

= 4√3 x² + 8x - 3x - 2√3

= 4x ( √3 x + 2 ) - √3 ( √3x + 2 )

= ( √3x + 2 ) ( 4x - √3 )

2 ) 32x³ + 108b³

= 4( 8x³ + 27b³ )

= 4 [ ( 2x )³ + ( 3b )³]

*****************

By the identity ,

a³ + b³ = ( a + b ) ( a² - ab + b² )

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= 4 [ ( 2x + 3b ) [ ( 2x )² - 2x × 3b + ( 3b )² ]

= 4 [ ( 2x + 3b ) [ 4x² - 6xb + 9b² ]

I hope this helps you.

: )