Question

if 12 and 11 = 23, if 18 and 16=68 than what is for 15 and x = 56​

Answer 1

$\boxed{Answer\:=\:13}$

Case ➡ 1

Given , 12 and 11 = 23

[Squaring the numbers]

12^2 = 12×12 = 144

11^2 = 11×11 = 121

[Subtract 121 from 144]

144 - 121 = 23

Case ➡ 2

Given , 18 and 16 = 68

[Squaring the numbers]

18^2 = 18×18 = 324

16^2 = 16×16 = 256

[Subtract 256 from 324]

324 - 256 = 68

Case ➡ 3

Given , 15 and x = 56

[Squaring the numbers]

15^2 = 15×15 = 225

x^2 = x × x = x^2

[Subtract x^2 from 225]

x^2 - 225 = 56

225 - 56 = x^2

169 = x^2

√169 = x

13 = x

$\underline{Therefore\:value\:of\:x\:=\:13}$

Answer 2

Solution :

First term : $\boxed{12}\underbrace{}_{\boxed{23}}\boxed{11}$

$\implies 12^{2}-11^{2}=144-121=23$

Second term : $\boxed{18}\underbrace{}_{\boxed{68}}\boxed{16}$

$\implies 18^{2}-16^{2}=324-256=68$

The formula can be generalised as

$\boxed{A}\underbrace{}_{\boxed{C}}\boxed{B}$

$\implies C=A^{2}-B^{2},\:A>B$

Third term : $\boxed{15}\underbrace{}_{\boxed{56}}\boxed{?}$

    We take ? = x

$\implies 56=15^{2}-x^{2}$

$\implies x^{2}=15^{2}-56$

$\implies x^{2}=225-56$

$\implies x^{2}=169=13^{2}$

$\implies x=13$

So, the third one be $\boxed{15}\underbrace{}_{\boxed{56}}\boxed{13}$

Therefore, the complete puzzle be

$\boxed{\boxed{12}\underbrace{}_{\boxed{23}}\boxed{11}\:\boxed{18}\underbrace{}_{\boxed{68}}\boxed{16}\:\boxed{15}\underbrace{}_{\boxed{56}}\boxed{13}}$