Question

Find the G.D.C and Lcm :
(x²-16),(x²-9x+20) and (2x²-128)​

Answer 1

Step-by-step explanation:

Given :-

(x²-16),(x²-9x+20) and (2x²-128)

To find :-

HCF and LCM of the given expressions?

Solution :-

Given expressions are (x²-16),(x²-9x+20) and (2x²-128)

I) x²-16

=> x²-4²

=>(x+2)(x-2)

ii) x²-9x+20

=> x²-5x-4x+20

=> x(x-5)-4(x-5)

=> (x-5)(x-4)

iii) 2x²-128

=> 2(x²-64)

=> 2(x²-8²)

=> 2(x+8)(x-8)

x²-16 = (x+4)(x-4)

x²-9x+20 = (x-4)(x-5)

2x²-128 = 2(x+8)(x-8)

HCF = 1

LCM = 2(x+4)(x-4)(x-4)(x+8)(x-8)(x-5)

=> LCM = (x²-16)(x²-9x+20)(2x²-128)

=> LCM of the given expressions

=( x⁴-16x²-9x³+144x+20x²-320)(2x²-128)

=> LCM = (x⁴-9x³+4x²-320)(2x²-128)

=> LCM = 2x⁶-128x⁴-18x⁵+1152x²+8x⁴-512x²-640x²+40960

=> 2x⁶-18x⁵-120x⁴+40960

Answer:-

HCF os the given expressions is 1

LCM of the given expressions is 2x⁶-18x⁵-120x⁴+40960