The binary operation * is defined by a^ * b=a^2+b^2+a b+1, then (… - Vidyadip

MCQ

The binary operation $*$ is defined by $a^ * b=a^2+b^2+a b+1$, then $(2^ * 3)^ * 2$ is equal to:

A
$20$
B
$40$
C
$400$
✓
$445$

✓

Answer

Correct option: D.

$445$

Given: $a{ }^* b=a^2+b^2+a b+1$
$2^ * 3=2^2+3^2+2 \times 3+1$
$=4+9+6+1$
$=20$
$(2^ * 3)^ * 2=20^ * 2$
$=20^2+2^2+20 \times 2+1$
$=400+4+40+1$
$=445$

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