Answer:
7
Step-by-step explanation:
Squaring the first equation gives ...
9a^2 + 2·3a·3/a + 9/a^2 = 25
The factors of "a" in the middle term cancel, leaving ...
9a^2 +9/a^2 +18 = 25
Subtracting 18 answers the question:
9a^2 +9/a^2 = 7
The value for the given expression:
[tex]9 a^{2}+\frac{9}{a^{2}}=7[/tex]
[tex]3 a+\frac{3}{a}=5[/tex]
First, we need to square both the sides of the given expression:
[tex]\Rightarrow\left(3 a+\frac{3}{a}\right)^{2}=25[/tex]
On applying the below algebraic identity:
[tex](a+b)^{2}=a^{2}+b^{2}+2 a b[/tex]
We get,
[tex]\Rightarrow(3 a)^{2}+\left(\frac{3}{a}\right)^{2}++2(3 a)\left(\frac{3}{a}\right)=25[/tex]
On squaring the terms:
[tex]\Rightarrow 9 a^{2}+\frac{9}{a^{2}}+2(3 a)\left(\frac{3}{a}\right)=25[/tex]
On cancelling the ‘a’ variable:
[tex]\Rightarrow 9 a^{2}+\frac{9}{a^{2}}+2(9)=25[/tex]
On multiplying the constants:
[tex]\Rightarrow 9 a^{2}+\frac{9}{a^{2}}+18=25[/tex]
On taking constant on one side and keeping variable on one side:
[tex]\Rightarrow 9 a^{2}+\frac{9}{a^{2}}=25-18[/tex]
On subtracting the constants, we get the final answer as:
[tex]\therefore 9 a^{2}+\frac{9}{a^{2}}=7[/tex]
