Question

A + 2 b is equal to 3 and a b is equal to minus 5 find the value of a square + 4 b square and a cube + 8 b cube

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Answer 1

Given:-

• a+2b=3-----(i)
• ab=-5------(ii)

To Find:-

• The value of a²+4b²
• The value of a³+8b³

Solution:-

• At first find the value of a and b by above solving equation a+2b=3 and ab=-5

=>a+2b=3

• Now solving ab=-5

=>ab=-5

=>a=-5/b

• Now putting the value of a=-5/b in eq 1

=>a+2b=3

=>-5/b+2b=3

=>-5+2b²/b=3

=>2b²-5=3b

=>2b²-3b-5=0

• Splitting the middle term here

=>2b²+2b-5b-5=0

=>2b(b+1)-5(b+1)=0

=>(2b-5)(b+1)

therefore, 2b-5=0=>b=5/2 and b+1=0=>b=-1

• Here negative value can't be kept so we take b=5/2

Now, putting the value of b=5/2 in eq 2

=>ab=-5

=>a×5/2=-5

=>5a=-10

=>a=-2

• Now find the the value by putting the value of a and b

=>The value of a²+4b²

=>(-2)²+4(5/2)²

=>4+4×25/4

=>4+100/4

=>16+100/4

=>116/4=29

=>The value of a³+8b³

=>(-2)³+8(5/2)³

=>-8+8×125/8

=>-8+1000/8

=>-64+1000/8

=>936/8=117

Hence,

• The value of a²+4b²=29
• The value of a³+8b³=117

Answer 2

Correct Question :

a+ 2 b is equal to 3 and a b is equal to - 5 find the value of a ² + 4 b ² and a ³ + 8 b ³.

Answer :

_______________________________________

Given :

• a + 2b = 3
• ab = - 5

________________________________________

To Find :

• a²+4b²

• a³ + 8b³

_________________________________________

Solution :

A.T.Q,

a +2b = 3

a = 3-2b..................... Equation 1

a ×b = - 5

From equation 1, we have

→(3-2b) × b = - 5

→3b - 2b² = - 5

→ - 2b²+3b + 5 =0

→2b²-3b-5 = 0

→2b² - 5b+2b - 5 = 0

→2b²+2b-5b-5 = 0

→2b(b+1)-5(b-1)= 0

(2b-5)(b+1)= 0

$Hence,b \: = ( \frac{ 5}{2}) \: or \: - 1.$

As negative values cannot be taken.

Let's take the value of b is 5/2. Then a = 3-2×5/2= - 2.

Now,

For, a ² + 4b²

$= > {(-2)}^{2} + 4 ({5/2))}^{2} \\ = > 4+4×\frac{25}{4}\\ = >29$

And for, a³+ 8b³

$= > {(-2)}^{3} + 8 ({\frac{5}{2})}^{3} \\ = > - 8+8×\frac{125} {8}\\ = > 117$