The solution of X &# 178; - | x | 6 ＜ 0

The solution of X &# 178; - | x | 6 ＜ 0


Let a = | X|
x²－|x|－6＜0
a^2-a-6



How is it most convenient to simplify [(X-8) & # 178; + Y & # 178;] = 2 √ [(X-2) & # 178; + Y & # 178;]?


Square
[(x-8)²+y²]=4[(x-2)²+y²]
x^2-16x+64+y^2=4x^2-16x+16+4y^2
3x^2+3y^2=48
x^2+y^2=16



(10-x)²+8²=10²


(10-x)²=36
So 10-x = 6 or - 6
So x = 4 or 16



How to solve X & # 178; - 2x = 80?


x²－2x＝80
x²－2x+1-1=80
（x-1）²=81
x-1=9
x=10
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