Calculator Killer 4

Algebra Level 3

$\large 100000^* - 99999^*$

We define the operator $*$ such that $A^* = A \color{#D61F06}{\div} A \color{#3D99F6}+ A \color{#20A900}{\times} A \color{#69047E}- A$ . Evaluate the expression above.

199998 200000 200002 200001 199999

2 solutions

Swagath N Shaji
Dec 19, 2015

A÷A=1 , A×A-A=A(A-1)=A²-A
A÷A+A×A-A = A²-A+1
Let A=100000 ,99999=A-1
100000.− 99999.
=A²-A+1-((A-1)²-(A-1)+1)
=A²-A+1-((A²-2A+1)-A+1+1)
=A²-A+1-(A²-3A+3) =A²-A+1-A²+3A-3 =2A-2 =2×100000-2 =200000-2 =199998

I did the same :)

Angel T. López - 5 years, 5 months ago

Saya Suka
Apr 14, 2021

A* = A ÷ A + A × A – A
= (A ÷ A) + (A × A) – A
= 1 + A² – A

100000* – 99999*
= [ 1 + 100000² – 100000 ] – [ 1 + 99999² – 99999 ]
= (1 – 1) + (100000² – 99999²) – (100000 – 99999)
= 0 + (100000 + 99999) × (100000 – 99999) – 1
= 199999 × 1 – 1
= 199998

Calculator Killer 4

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