Question

X + 5y = 9 and xy = 4 find the value (×^2 +25y^2)

Answer 1

ANSWER:

• Value of x²+25y² = 41.

GIVEN:

• x+5y = 9
• xy = 4 ....(i)

TO FIND:

• Value of x²+25y²

SOLUTION:

=> x+5y = 9

Squaring both sides we get:

=> (x+5y)² = (9)²

=> (x)²+(5y)²+2(x)(5y) = 81

=> x²+25y²+10xy = 81

Putting xy = 4 from (i)

=> x²+25y²+10(4) = 81

=> x²+25y² +40 = 81

=> x²+25y² = 81-40

=> x²+25y² = 41

Value of x²+25y² = 41.

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab