Evaluate and simplify the expression when [tex]\( x = 4 \)[/tex] and [tex]\( y = -3 \)[/tex].

[tex]\[ \frac{64}{x^2 + 2y^2 - 2} = [?] \][/tex]



Answer :

Let's break down the given expression step by step and evaluate it for [tex]\( x = 4 \)[/tex] and [tex]\( y = -3 \)[/tex].

Given expression:
[tex]\[ \frac{64}{x^2 + 2y^2 - 2} \][/tex]

First, we need to determine the values of [tex]\( x^2 \)[/tex] and [tex]\( y^2 \)[/tex]:
[tex]\[ x^2 = 4^2 = 16 \][/tex]
[tex]\[ y^2 = (-3)^2 = 9 \][/tex]

Next, we substitute [tex]\( x^2 \)[/tex] and [tex]\( y^2 \)[/tex] into the denominator of the given expression:
[tex]\[ x^2 + 2y^2 - 2 = 16 + 2(9) - 2 \][/tex]

Calculate [tex]\( 2(9) \)[/tex]:
[tex]\[ 2 \cdot 9 = 18 \][/tex]

Now, adding and subtracting these values:
[tex]\[ 16 + 18 - 2 = 32 \][/tex]

Therefore, the denominator of the expression is 32.

Now, substitute this value back into the expression:
[tex]\[ \frac{64}{32} \][/tex]

Simplify the fraction:
[tex]\[ \frac{64}{32} = 2 \][/tex]

Hence, the value of the expression when [tex]\( x = 4 \)[/tex] and [tex]\( y = -3 \)[/tex] is:
[tex]\[ 2 \][/tex]