Question

Find a2-b2 if a-b=.9 and ab=.36

Answer 1

HEYA !

Given that,

a - b = 9 and ab = 36

We know the formula

(a + b)² = (a - b)² + 4ab

On putting given values , We get

(a + b)² = 9² + 4×(36)

→ (a + b)² = 81 + 144

→ (a + b)² = 225

→ (a + b) = ±15

Now,

★ When
a - b = 9 and a + b = 15

→ a² - b² = (a + b) (a - b)

→ a² - b² = 15 × 9

→ a² - b² = 135

★ When
a - b = 9 and a + b = -15

→ a² - b² = (a + b) (a - b)

→ a² - b² = -15 × 9

→ a² - b² = -135

HENCE,

a² - b² = 135 or -135

Answer 2

Heya !!!



A- B = 9 ---------(1)


AB = 36 ----------(2)


From equation (1) we get,


A - B = 9


A = 9 + B -----------(3)



Putting the value of A in equation (2)


A × B = 36


(9 + B) × B = 36



B² + 9B -36 = 0


B² +12B -3B -36 = 0



B(B+12) -3(B+12) = 0


(B+12) (B-3) = 0


(B+12) = 0 OR (B-3) = 0



B = -12 or B = 3



Putting B = 3 in equation (3)



A = 9 + B


A = 9 +3 = 12




Therefore,


(A²-B²) = (A + B) ( A - B) => (A)² - (B)²




=> (12)² - (3)²


=> 144 - 9


=> 135



HENCE,


(A²-B²) = 135



HOPE IT WILL HELP YOU....... :-)