Question

factorise if a+b=7 and ab=6 find a^2 -b^2​

Answer 1

Answer:

35

Step-by-step explanation:

(a+b)=7

squaring on both sides

(a+b)²=7²

a²+b²+2ab=49

Multiplying by(-4ab) on both sides

a²+b²+2ab-4ab=49-4ab

a²+b²-2ab=49-4×6

(a-b)²=49-24

(a-b)²=25

a-b=√25

a-b=5

now, a²-b²=(a+b) ×(a-b)

=7×5

=35

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