Question

5. Show that (a - b)2, (a? + b2) and (a + b)2 are in AP.
6. Find three numbers in AP whose sum is 15 and produ:​

Answer 1

$\huge\bigstar\sf\red{Answer:}$

$\sf{t_{1}=(a-b)^{2}=a^{2}+b^{2}-2ab}$

$\sf{t_{2}=a^{2}+b^{2}}$

$\sf{t_{3}=(a+b)^{2}=a^{2}+b^{2}+2ab}$

$\sf{Here,}$

$\sf{t_{2}-t_{1}=a^{2}+b^{2}-a^{2}-b^{2}+2ab=2ab}$

$\sf{t_{3}-t_{2}=a^{2}+b^{2}+2ab-a^{2}-b^{2}=2ab}$

$\sf{Hence, \ t_{2}-t_{1}=t_{3}-t_{2}}$

$\sf{Hence, \ (a-b)^{2}, (a^{2}+b^{2} \ and \ (a+b)^{2}}$

$\sf{are \ in \ AP.}$