Question

if a+b =7 and ab = 6 find the value of a^2 - b^2​

Answer 1

Answer:

±35

Step-by-step explanation:

a+b=7

a=b-7

Substitute in ab=6

(b-7)b=6

b²-7b-6=0

b²-6b-b-6=0

b(b-6)-1(b-6)=0

b=6 or 1

When b=6

a=1

So a²-b²=-35

When b=1

a=6

So a²-b²=35

Hope it is helpful

Answer 2

$\huge\red{\tt{Question:-}}$

If a+b and ab=6. Find a²-b².

$\huge\green{\tt{Answer:-}}$

${\tt{\boxed{Given:-}}}$

⠀⠀⠀★ a+b=7

⠀⠀⠀★ ab=6

${\mathcal{\boxed{To~find:-}}}$

⠀⠀⠀★ a²+b²

${\mathcal{\boxed{Identity~Used:-}}}$

⠀⠀(x+y)² = x²+y²+2xy

Here,

⠀⠀⠀★x=a

⠀⠀⠀★y=b

$\huge\purple{\tt{⇝}}$ (a+b)²=a²+b²+2ab

$\huge\purple{\tt{⇝}}$ (7)²=a²+b²+2×(6)

$\huge\purple{\tt{⇝}}$ 49=a²+b²+12

$\huge\purple{\tt{⇝}}$ 49-12=a²+b²

$\huge\purple{\tt{⇝}}$37=a²+b²

$\huge\purple{\tt{⇝}}$ a²+b²=37

∴ a²+b²=37

∴ Your Answer=a²+b²= 37